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My university administration pushes all lecturers to apply to competitive grants from a national science fund. I am new to this and do not know how to start. So I thought to ask my previous advisors, or senior lecturers in my department, who work in related topics, and received such grants in previous years, to send me their past applications to the same fund. This may help me a lot to see how a successful application looks like.

However, I fear that this might be perceived as rudeness, since my application competes with theirs. The fund is very competitive, and if I send a competitive application, it reduces their chance to win a new grant. It's like asking a competitor in a code competition to show me their code..

Is it really considered rude to ask other researchers for their previous grant applications?

In my experience in both the US and UK this is quite common, and in fact encouraged. While technically, we are all in competition for funding, research works best when it is collaborative. There are so many nuances in a grant application that vary from across funding calls, that seeing successful (and even unsuccessful) applications can be hugely beneficial. they can give you an idea as to the scope of the project, how much it should build on previous work, and how much preliminary research should be done prior to applying.

I would hope current and past colleagues will share their funded proposals and would never hesitate to ask, and in fact would be mildly offended if they did not share them. Unfunded proposals are often helpful to see, but some colleagues are more hesitant to share unsuccessful ideas that they may still be trying to improve. In addition to asking to see proposals, you should be asking for feedback on your proposal as well as offering to read the proposal's of colleagues.

One aspect of a grant proposal that is difficult for new investigators (okay they are all difficult), is the budget. Many PIs will not share the budget of the proposal with others since they include salary information that many people consider private.

For national funding there exist often official detailed guidelines about expected/prescribed length, style, content, outline of the application. You probably also find inofficial guidelines on single university servers by googling (filetype:pdf, inurl:edu)

Very similar rules of thumb as for writing a paper and getting it through the review process apply: No redundancy, logical consistency, clear structure...

And like publishing papers you learn it by doing. If you never wrote a paper and try now to write your first one and submit it to nature/science, reading a former nature/science article even about research of your field will not help you a lot. In the best case someone who reviewed for that journal takes a look on your paper, which is often the professor.

The big difference to writing papers is the section about your financial/working plan. How much money do you need and for what. This needs advise from experienced PI's, otherwise you might even in the case of funding end with much less than you need to successfully conduct the project, as often only a fraction of the requested money is granted.

Contrary to a journal review, the examiners scrutinizing your application are often no real experts in your field of research, as the pool of reviewers for national funding is much smaller. Therefore, the level of comprehension of the examiner will not be as high as compared to a journal reviewer and you have to write your aplication accordingly. Depending on the goal of your project (fundamental research, prototype -> TRL level), more scientific/technical/economic reseasoning and planning is necessary.

If you have experience in writing papers, I don't think reading old applications will help you a lot and improve your application significantly, as the application guidelines often set so much constrictions to describe your project in the necessary shortness. And if not, I think you might waste a lot of time without an experienced reviewer of your application.

I would also rather suggest to you to take courses on project managment at your university. In the end not the better scientific idea gets the grant, but the project that seems to be well planned and has all obstacles and details foreseen and listed with an according project/financial plan.