Implementation of TGPX
 

I decided to try TGPX on one of my domains. I installed the script into tgpx subdirectory, changed premissions and everything, but I still have no idea how to dispplay the pages with galleries. Any tip?

I assume you've done all the initial configuration and have at least one page template. It comes with a default template, but it's pretty bland.

build all - rebuilds all existing pages with galleries set to used or holding.
build all with new - rebuilds all existing pages using galleries set to approved, then used or holding as needed to fill the page.

pending galleries will not be used until they are approved.

The included documentation is pretty comprehensive. It covers the commands and available database variables quite well. There is a user run support forum as well http://forums.unofficialjmbsupport.com/index.php

Correct.

My problem is, that I can't create page (TGP Pages -> Manage Pages -> Add TGP Page) even if I create such directory/file manually and change its permission... Auto creation doesn't work even all the permissions seem to be properly set.

It sure sounds like a permission issue. I'd suggest a search of that support forum to see if anyone else has had a similar problem.