How many questions with same script can I ask, if code not only merged reviews but adds new functionality?
If it has new functionality (or even when it doesn't but it has been rewritten significantly enough to be new code), there's no problem with posting a new version. We've seen questions with 5 versions of the same program, every time a bit better.
Can I submit part of code(fully working part with new code) together with full code or without(but with github link)?
With the full code, yes. Links are acceptable for bonus context, but everything you want to have reviewed has to be included in the question itself. Not behind links.
Will it make users bored? :)
Perhaps, perhaps not. If you put in the effort to improve your code and listen to the answers provided, I'm sure there are enough people willing to put in the effort to help out.
Just make sure you leave a couple of days (a good rule of thumb is to wait at least 48 hours, preferably more) between posting revisions. More answers might be incoming after all.