Trjtdtk

If we want to say that A depends on none but all depends on A. A needs no one but everyone needs A. What is the best word that fits best this trait?

1. Independent


2. Self-reliant


3. Self-sufficient

Let me give my own research that the word 'independent' seems to be covering this particular trait a little less than the other two.

All (independent, self-reliant, self-sufficient) are suitable to say: "A depends on none" or "A needs no one".

However, I am not aware of a word to mean: "all depends on A" or "everyone needs A".

The technical terms in theology are:

• 
  First Cause — as given in another answer, although theologically this does not encompass being more than the "Alpha", the thing that caused everything else, rather than the thing upon which other things' existences continue to depend after creation.


• 
  necessary — A necessary being is defined as one that has no cause for existence, and simply must exist by its very nature. Again, however, this does not imply that other things are contingent upon it.


• 
  non-contingent — the opposite of contingent, i.e. caused by something else. It's not the same as necessary because non-contingency simply means not depending upon something else for existence; it does not incorporate the notion of existing by definition. A non-contingent thing has no dependence; it however does not necessarily exist.


• 
  a se — an older theological term from which aseity is derived, the state of self-causation or self-dependence, a necessary being that is (also) contingent upon nothing more than itself.


• 
  Prime Mover or Unmoved Mover — an even older term from Aristotle et al. that encompasses both parts of the question, as the concept here encompasses being the source of all motion (i.e. change and cause, the original term encompassing more than what "motion" does today) in the universe.

I'm not going to even attempt to give more exact definitions. There are millennia of writings on these and exactly what they are, from Aquinas, Anselm, and Aristotle, through Spinoza, to Zappa. ☺

The normal way of expressing this is to say that God is the first cause (of everything):

[Merriam-Webster]

: the self-created ultimate source of all being

That encompasses all of the meanings you want.

Self-Sufficient would be most appropriate as the word clearly describes that A is not dependent on anyone for anything and he alone is sufficient for himself.

You would say that God is not "independent" (that would suggest that some other entity is trying to politically control him but he does not have to abide by that), but rather is self-sustaining (and additionally that God sustains everything else), for that sort of intrinsic dependency on another being for one's existence and survival.