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If they want to act as high schoolers, you'll need to treat them like high schoolers.

I've taught in high school for a little time and while your semester already started, it is not too late to get a handle back on your class. The first few minutes after the class start is the most important moment to make it clear messing around will not be tolerated.

I would try at least once, at the beginning of a class, to say something like this :

You guys are being hard to manage and I'm sure you're aware of it. You are being disrespectful towards me, the rest of the teaching staff and other students who are trying to work. I'd like to know what is wrong, is there anything you think might make your experience better?

This way, you make it clear you want to work with them to find a solution and that it is bothering many people. Give them a chance to work it out with you before going the "full authority" route. You might give some troublemakers to turn into "positive leaders".

Even if this works, you need to start making it clear who has authority in your class. When you start your class, state your rules and don't move away from them. You'll probably need to set an example a couple of times before your students understand. You need to systematically apply the rules you gave your students or else they'll start exploiting you.

Regarding what you said in your post :

People asking literally the same questions over and over

Offer the student to come see you after class if they asked a question that was already asked, this way you do not slow down the pace of your class and if it's an attempt at "trolling" the student simply won't come to see you.

Blatant plagiarism

Your school clearly has a policy against plagiarism, start using it without exception. These students lost their right to second chances. If you catch plagiarism, report it to the correct instance at your school and let the comity in place decide.

Students pretty much insulting the lecturer and staff or laughing (sometimes at others asking questions)

Respect is the most important thing in a class. If a kid in high school (where, at this age, education is a right not a service) can get kicked out of a class for being not being respectful, so can an adult. If I paid 10k$ for a class, you can be damn sure I'd stop this after being kicked out once. If you want to make sure you won't have repercussions, go see the head of your department to make sure they have your back if something happens.

Being noisy during lectures

To be fair, this can happen. If this is repeated, refer to the point above.

You said in a comment "That is a straightforward solution but the lead instructor in this case does not want to take authoritarian measures. So that's another challenge here". This is sad but University teachers aren't often good at managing this kind of class (because they don't have much experience with them). You should try talking to him/her about it, stating that it really messes up the flow of the class, the confidence of all the teaching staff and the overall credibility of the class.

As a last resort, when your class gets out of control, stop talking. More often than not, the students will deal with themselves and silence should come back to the class. If it doesn't well it is their loss.

To make this work, the best case scenario would be for the whole teaching staff to be on the same line and to make sure your boss has your back, but University students are customers of a service under certain conditions. If some students mess up with your class, they interfere with the students who are respecting the rules and this is not acceptable.

This happens to almost everyone who teaches in academia. We all eventually get "that class". Let me lay out some options for you:

Look for experts on your campus outside the department

First of all, if you have a college of education at your school, head over there and find a professor who was a former K-12 teacher. Further, if your school has a teacher prep program, you are in even better luck. There will likely be a few teaching veterans who have plenty of experience getting unruly classes (kids to adults) back under control. Some of those education professors who were former teachers have classroom management down to an art form. It can be really interesting to watch how effortlessly they do it as well. I recommend reaching out to the department head there and asking if there is a professor (or even graduate student) who might be able to give you some advice.

Look for advice in your department

Ask others in your department if they have had a similar situation. Reach out to the department head. First of all, it might be best to fill your department head in on whats going on anyway. I have not known too many department heads who like surprises. Especially surprise calls from administration asking what they know about students complaining being kicked out of a class they paid $10,000 for.

Self Fix it

Grab a book on classroom management and see what you can do on your own. Its tough getting a class back in line mid semester, but there is plenty of help advice in books and from blogs. The usual remedy is to implement increased structure in the class. Get the class into doing routines.

Remember, kicking out a student from class is not what you want to do. Banning a student from class is the nuclear option. Once you go down that route, things get out of your control. You might end up with an administrative problem. This gets even worse if you end up kicking the wrong person out. How are you going to even determine who is the ring leader in the first place?

I'm afraid that, as a TA there is probably very little you can do. The instructor might be able to do something and there are some suggestions in the other answers here that can help, but you need a certain amount of recognized authority to make it work.

I have had to deal (once) with an equally difficult, though different situation. I was able to handle it with a "shock therapy" trick, but only because I was a senior professor at the institution. A junior faculty member probably wouldn't be able to make this work.

In my case, the students weren't disruptive, just disengaged. They didn't take notes, didn't seem to study, didn't ask questions. Completely passive. I asked one student before class why he didn't take notes and he just pointed to his head as if he learned everything immediately without effort. Of course it doesn't work that way.

My solution was to announce at the beginning of a class that I was willing to just fail everyone in the class and we could all stop pretending. I would stop pretending to teach, they would stop pretending to learn, and we wouldn't even have to waste the time coming to class.

Shock and dismay.

The real problem is that most of them had had an easy time up to then with their education and no one had challenged them very deeply. It wasn't that they were lazy but just that they didn't really know how to learn. So I spent a couple of classroom hours teaching them how to learn. This was in a second year Computer Science course, by the way.

The problem the OP states is different, but, with sufficient authority, recognized by the university, if not by the particular students, a shock therapy might work. Walk out of the classroom at the first sign of disrespect. Ask a disruptive student to immediately carry a note to the department head and wait for a reply. The note would mention the disrespect. Announce a snap quiz. Make it hard.

Very risky.

In my case, the story went around the department and added to my mythical powers. The students improved. The time and effort wasn't wasted.

But, if you try this, you'd better be certain that you will be allowed to follow through and that the department will back you. A junior member of the faculty would be advised to try it only with permission of the head and, in the current situation, concurrence of the staff of the course (all TAs).

Identify the troublemakers and eject them from class as soon as they step out of line. As you say, this kind of situation often snowballs out of a few bad elements. These students are not there for entertainment and this isn't a high school. Someone who doesn't want to learn isn't worth wasting any time. Removing the bad elements might help restoring a professional environment, keeping only people who are actually intent on learning the content of the class.

Usually these students end up getting the hint. If they don't, ban them outright from the class after a few times. The other students deserve a quality course from you and the other teachers, and these troublemakers are preventing it. It is highly unlikely that the whole class is really "cynical", and you will be left with actual students, not people who want to pass the time. In the rare event that literally all of the registered people don't care about the class, congratulate yourself on getting paid time off and watch movies or read a book during scheduled class time.

Now, since you used a dollar sign, wrote "top 10" and mentioned students "paying $10k", I'm pretty confident that you are in the US, so take my advice with a grain of salt. I am not from the US and it is my understanding that the motto "customer is king" permeates even non-mercantile aspects of society such as higher education. If these troublemakers try to get a refund which in turn provokes the administration into pushing back on your decision to eject/ban students, try to make the argument that movie theaters are well within their rights to kick out noisy spectators and not refund them anything. But in the end, it's up to you to decide whether the fight is worth it and whether you have the political clout to pull this kind of stunt.

If it were 100% of the class acting this way, I'd say you have some time to experiment and find the best way to fix things. But, if there has been a single student that has acted properly and done their due diligence throughout the semester, I think that makes a big difference.

If I were a student in this class who was not participating in counterproductive behavior, I would rely on the instructors acting quickly to ensure I was still getting the quality of education I deserved. I would (personally) not want to experience a few months of professors experimenting with different disciplinary methods. If the situation above is accurate, this would be the point at which I'd already be reaching out to administration for a refund or class reassignment and I'd specifically say "the professors can't control the class" even though the class itself is intentionally out of control.

If 80% of the class can't conduct themselves in class properly, I would expect them to be asked to leave. If you can construe this as an absence, then they have a finite number of removals before they automatically fail. If it's for disrespecting staff or other students, I can't imagine there being much pushback if you can get the person who was disrespected to sign a paper saying it happened.

Instituting class conduct rules, with definite consequences for breaking them, is also a quantifiable way to show your expectations and their lack of respect for them. The bottom line is that if you have to take disciplinary action at this level of academia, prepare for it to be challenged, so back it up with quantifiable evidence (not anecdotal).

Also, given the course"s topic, as a student I would respect the logic of saying "Some of you can't figure out how to conduct yourselves professionally amongst your peers, which is also the topic of this course. Classroom performance counts for 51% of your grade." I feel like that's a no-brainer, like you said, it's not just some core requirement they'll have to repeat, they are purchasing their own F a la carte. Remind them of that.

Not wanting to use authoritarian methods is admirable, but the longer you wait the more legitimate complaints you may get from the few students who want to be there and are making the proper effort. I think the burden is on you to show (starting very soon) you have enacted policies to combat, if not solve, the problem. If not, you (or the profs) could be held responsible for legitimate students asking for a refund, which is worse than disciplinary cases asking for one.

Well, I think the crucial information here is in the comments to the post, which reveal that the root cause of the problem is big difference in the skill levels between the attendees, the lower skill level guys happen to be managers who are accustomed to be outspoken and steer the conversation out of it's professional realm.

In this case, the reasonable solution will be dividing the classroom and providing for each skill group appropriate information, so that for all groups the pace will be manageable.

It will likely require time investment in creating two parallel curriculums. Also assignment levels may vary according to the skill set.

The managers are also likely interested in different aspects of the data science from the programmer guys, so it's reasonable if they will show their discontent about spending time on the material which has less value for them.

Additionally, an approach for smart kids at school may work, if the managers' ego will permit it - make time for workshops, and when working on assignments, make the people who catch the material faster, help the guys who struggle. If done well, it may prove a valuable experience for all the participants.