IITM - Indraprastha Institute of Technology and Management

https://www.shiksha.com/college-predictor
Please check this link for better results.
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No, IITM Janakpuri doesn't ask for mathematics. Only 50% in +2 is required for admission.
If you want to learn programming languages which you will be studying in your BCA course then you can check out this app "BCA - Course Programming" which is specially designed and developed for BCA students and is available on Google Play Store. 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.

You can visit this link:
https://www.shiksha.com/college-predictor

It is a government college.

Yes, of course, students can get education loan but his parents need to apply in Bank for this.
They will give you a loan on your degree and you can pay it according to the time given to you.

It depends on the college's admission process but most of the college needs at least 50% in 10+2, their rank cutoff changes every year.
HERE IS THE ELIGIBILITY
Passed 12th Class of 10+2 of CBSE or equivalent with a minimum of 50% marks in aggregate with pass in English (core or elective or functional) and Mathematics or Computer Science/Informatics Practice/Computer Applications.
OR
Three-year Diploma in a branch of Engineering from a polytechnic duly approved by All India Council for Technical Education and affiliated to a recognized examining body with a minimum of 50% marks in aggregate.

The degree can only be provided by an University and the name of the affiliated University would be indicated when you receive your degree, if your college is affiliated to IP University then the degree certificate would bear the name of IP University