Can a candidate apply for the one-year Diploma in the professional photography course after s/he has graduated?

You can apply for it if you are interested but if you have done your graduation from another field like B.Com or any other then it is not useful for the candidate. If the candidate has done hi her graduation from the photography line, then it will be useful for them and it also helps them in getting

Yes, of course you can. There are many institutes that provide such Diploma courses.

Yes, anyone can opt for professional photography course whenever she/he wants to.

Yes, a candidate can apply for it.