MCA

Mostly integrated like B.Tech+MBA, B.Tech+M.Tech etc is of 5 years tenure but in case of BCA+MCA, it's always 6 years.

Both are equally good. The MBA people are more known for their business tactics and they help in uplifting the business organisation of the company. MCA people grab the technology part to cope up with the company's business needs. They both accentuate a company's profits. Regarding salary, MBA people get more than MCA since they help in reviving the business policies of the company which straightaway leads in to profit (If modeled correctly). You didn't mention your graduation stream so its difficult to know your inclination. But if you are into technology also you may go for MBA in IT/Engineering to fulfill it.

In which state do you seek admission?

The fee structure of MCA is:
1st year: INR 58800
2nd year: INR 50000
3rd year: INR 50000
Total: INR 158800

ABCL/c+ uses asynchronous message passing among objects to achieve concurrency. It requires Common Lisp. Implementations in Kyoto Common Lisp (KCL) and Symbolics Lisp are available from the author. Python manages dynamic type system and automatic memory management.

Year 1 = 70,347
Year 2 = 70,347
Year 3 = 70,347
Total = 211,041
From outside, you can't judge any college in right way. Every colleges post their placement record always higher than they can provide.
You can opt it MCA. It is not bad. It having some good record also.
Hope you have satisfied with my answer. If yes, then do upvote.

No, Loyola does not offer correspondence MCA course, it only offers regular MCA, follow the link below for details:
https://www.shiksha.com/college/loyola-college-lc-chennai-nungambakkam-1108/courses?bc[]=103&ct[]=64&lo[]=456

Yes, you can if you have maths in HSC.

Yes, there are few colleges which dosen't require maths in 10+2 but if you applying for MCA then you have to study maths in BCA, and its easy to study maths.