MCA

Yes, The All India MCA Common Entrance Test (AIMCET) is the entrance examination generally conducted by IIT's for admission to Master of Computer Applications (MCA) Program offered by IIT's and many leading Universities and Colleges.
Candidates with a Bachelor's degree of minimum 3 years duration in any discipline with Mathematics at the (10+2) school level or at the Bachelor's level are eligible.
But you may pursue MCA in other private college because AIMCET is not mandatory there.

yes commerce stream is backbone of mba mca &ca

don't get confuse you can go for mba

Both are good. But mca has comparatively good career options

Answer is yes little bit but you know what in these days job market, this full-time and distance education discrimination doesn't matter much.
If you choose a renowned and recognized distance education institute then no problem at all.

Yes you can do becouse you also knowing about the computer knowlage & it is part of them

yup u can go, bt need logical knowledge otherwise u can't understand programming language, i am frm mca.