This kind of issue is hard to track down without having access to the forum in question. Can you reproduce it on this site?
So the problem is i have 159 results. First page is good, but when i try to pass any other page i have no results.
You mean clicking the pagination buttons?
Experimentally i found that problem in the number of search keywords.
What specifically did you test, and what, exactly, was the result?
Should i use any other delimiter instead of spaces or it's a bug?
Spaces are correct.