I am currently completing a PHP & jQuery related project and I'm interested if I can post a question on Stack Overflow so other programmers and developers from specified technologies could rate it, advise, review, test, suggest, etc?
Stack Overflow is not a discussion forum, nor some kind of social networking site. It's a Q&A site. Any attempt would likely be seen as a form of spam by the community. Rather post it in some discussion forum or a social networking site.
If you see on Stack Overflow a question which could be answered by using your library, then you can always post an elaborate answer how to solve it without the library and then in the end recommend in a neutral way your library as a possibly more easy solution. Do it only for active questions though and don't actively look for old questions and bump them up in a too short time with copypasted answers. That would also be seen as a form of spam.