Is it possible to add a module to a K2 category page? I want to add all kinds of modules but am having trouble. The modules that I have selected to appear on all pages appear but the ones which I have chosen to appear on selected pages do not appear on K2 category pages because in the module page, K2 category pages do not show up.

you might try setting the module on "all pages" first then take the groups you dont want off
If you need modules in difficult places try modules anywhere by nonumber.nl