Most, if not all bullpup and submachine guns make for excellent CQB weapons. Bullpups give you that long barrel you get in standard AR rifles for accuracy, but the action is located further back by your shoulder making it shorter, and very pointable. Things like the L85A2, F2000, TAR (although that ones a bit hefty), FAMAS etc. make good CQB and long distance weapons. The P90 is a bullpup PDW and also excellent for CQB. I myself use an MP5 with a retractable stock and I mainly play close quarters. I am VERY happy with it, the stock can be adjusted for stability vs maneuverability but since I have a suppressed version, it's a little longer than normal. But I can always take it off
Then of course there are your side-arms and they are VERY handy in CQB
Generally anything short or bullpup is excellent for CQB.
As for specific weapons in your price range, I would have to do some research. 150 is really low end. Most people spend £200+ on a decent primary. My side-arm cost about £140!
Basically yes. The chamber and "action" with all the moving parts are located in the stock or further back.
If you play CoD you might know of this guy, who explains it quite well using an L85A2 (more commonly known as an SA-80). Although this is mainly for entertainment
theres a guy selling on West Yorkshire Airsoft Trading Community on facebook new not bought from him yet but will be soon i dont know him not recomending him just letting you know.