what times we can be sure that our all-in strategy is one of the nearest
to optimum profitable one? I can ask this question as two other questions. when we should push All-in for bluffing? and when we should push All-in with best hand?

If by optimal you non-exploitable, you can use the nash equilibirium charts. Non-exploitable strategies, though, are not best at exploiting opponents.

If by optimal, you maximally exploitive of opponents unbalanced play, that is going to be dependent on the specific game situation.

when you bluff you want to bet the amount that gives you the best chance of winning most times without adding more that doesnt help.

when you bet for value you want to bet the amount that is most likely to get called in most spots.

sounds simple and it is.

Simplifying a bit, but when we think we won't be called, and when we think we'll be called

yeap, that's more simplified and exactly what I mean.
what do you think about the answer? what is your idea about this 2 questions?

I’m going to post an initial pure math approach, but without any direct optimality consideration.

Assume pot = P and effective stack is B,which is what you will bet. The EV equation is

fe*P +(1-fe)(eq(P+2B)-B)

fe is fold equity(prob. villain folds) and eq is card equity (prob. hero wins if V calls)

Now given fe, you can solve for what equity you need for +EV or vice versa.

Then you can show for EV>= 0

eq >= 1/(P+2B) * (B –feP/(1-fe)) (I hope I got this right, it matches the result I got with a program)

Example: P = 100: B= 300: fe = 20%

Plugging in the above values, you need equity of at least 39.3% to make the shove.

Ok, but how good is your fold equity estimate or how certain are you that you have the needed equity, or could you do better with a check raise, etc. etc. ? So, the math can set up some boundaries and then the poker art comes into play to make adjustments to account for factors the math doesn’t consider.

Edit Regarding bluffing if you set eq=0, then you need fold equity of at least B/(P+B), which has been termed Alpha. For the example, a bluff shove needs fold equity of at least 300/400 = 75%