Can my landlord deduct painting and carpet cleaning from my deposit?

No... he can only do that if you damage the property hence damage deposit... if you have cats and the next person moving in is allergic then it might fall into that category since carpet have been contaminated with cat hair and it needs cleaning.

Depends... he can for the carpet cleaning if you can't prove it was professionally done before you left, particularly if its heavily soiled or stained... as far as the paint. Typically no... unless of course you breached the lease and left before it was over then they could... or if you had done something like paint it a dark or bright color, had stripes or something other than the color it was when you moved in.

If you soiled the carpet, often perhaps a pet, or you spilled something on the rug, did you have a carpet cleaner come in and clean before you left ?

Paint, did you smoke in the house ? Did you leave marks on the walls.