So first like opening goes to the corner, to the side and then center…
What questions i should ask of myself when i play to the whole board if i don’t need to respont to my opponent’s move locally? How i decide it ?
This is what Haylee thinks about but Haylee doesn’t say where to play tenuki or if i have sente and i can start to think where to play.
This is a hard question. The hardest question, really. To make good decisions, you must have a clear understanding of how each possibility will play out, and how those possibilities will influence the whole board, and how much they will be worth. Positional judgement, in other words.
That said, in general your priorities will look something like this:
1: If you have a weak group, fix it.
2: If your opponent has a weak group, attack it.
3: Play the biggest move. These tend to be:
a) Very early in the game, often the largest empty side.
b) Reducing or expanding in sente
c) Moves that expand and reduce at the same time
d) Invading, or preventing an invasion
The strategy stated in the OP applies to standard, 19x19 boards. It does not apply to 9x9 games, and may not apply to other board shapes or sizes.
good point. If anyone was interested in 9x9 (and didn’t know it already) we have this lovely book shared among us: https://www.dropbox.com/s/2kc0mtajqfvkyow/81_little_lions_an_introduction_to_the_9x9_board_for_advanced_beginners.pdf?dl=0
Is there same kind of book or manual for the 13x13 board? What are the principles for the 13x13 board?
none that I know of unfortunately. The only consensus seems to be, that center isn’t worth much on 13x13 
In other words, play primarily for territory rather than influence.
Look for where you would not want your opponent to play; take your opponent’s point of view and look for where you (he) would not want you to play.
I’ve lost a lot of 13x13 games by getting shut out of the center. My personal feeling is the balance of territory/influence is about the same as 19x19, but I’ll also concede mine is a minority view. 
I’m gonna try this rose thing:ramen:
Gerald Westhoff’s “Four Questions To Decide Your Strategy”
(The flowchart there has been added by me, after he visited me once and told me about them.)
Of course these are just rules of thumb, and they leave lots of questions open, like “what is weak”, etc., but I like them as simple guidelines. Some have said these are only good for DDK, but, having just scratched at SDK, I cannot judge this.