Guru Gobind Singh Indraprastha University

Yes, you can change the college, but they will deduct your security money.

Yes, you can pursue your BCA from IP University. As you have done maths in your +2 then you are eligible for admission, just make sure that your class 12th percentage is atleast 50% before seeking admission into IP University. Then you can get admission in for BCA. If you want to learn programming languages which you will be studying in your BCA course then you can check out this app which is specially designed and developed for BCA students. It has programs and assignments of languages like C, C+ and Java with their outputs. You'll be studying these languages in your 3 years of BCA.

GGSIPU conducts its admission through its own exam conducted every year in the month of June/July. You have to check the eligibility criteria fur appearing into the exam which changes every year but most of the time it remains 40% minimum.

You can expect your rank to be around 14-15K, and in the OBC list, you can expect to be at 3-4K.

I'll prefer you to opt for the MAIT as this is the best choice then any other colleges from the above mentioned list as this is the best college in terms of faculty, infra and also in the placements.

You should opt for UPES as in IPU, getting any good college at this rank for an outside Delhi student is not possible.

No, it is not mandatory to opt for maths in class 12th for the admission in B.Com.

Hello Riya,
Lateral entry is for Diploma students not for engineering students, changing colleges affiliated from different university is not as easy as it seems, however you may talk to colleges if they don't have any problems you can switch, but the chances are very low.
All the best.