please note I am speaking about tourist and buisness visa extentions.

to get an extention you need the usual paperwork for the visa type you are getting, you need proof of residence this could be a hotel or apartment the hotel must give it to you if asked you get the apartment from the psb after you register (24 hours) if you wait to long to register they could give you problems maybe a fine and very unusual but possible deportation.

you can get 1 extension when I last did it you could only get 30 days this might have changed and might be different depending on your home country.

you can not get a new L or M visa in Hk if you have been in china for even a few months regardless of the paperwork you present getting a work visa in Hk is still possible last I heard.

to get a new L or M visa you might have to go to thailand or another country or possibly your home country plan accordingly