MCA

BITS do not have or offer MCA in their course offering. You can try for private or BITS, Pilani for MCA.

5 years is a long gap, so I would suggest you to try to get some online course of some language like c, phyton, or if you can build interest in AI then it would be great as A. I. is in demand nowadays, and you will easily get certified courses of 6 months online as well as offline.

There are many all over the country, but first you need to give PGCET exam to get top colleges.

I think distance learning is an option for this type of situation. Sikkim Manipal University is one of the best institutes for this. Kindly check the distance learning programme of the universities.

There are a lot of good college for MCA in Pune. Visit the link given below and checkout the lists, placement record, academics etc.
https://www.shiksha.com/it-software/colleges/mca-colleges-Pune
Good luck.

No, it provides full time 3 years MCA course.
Good luck.

Yes,
There are two colleges in Bangalore:
Yalahanka BMSIT -This is not autonomous college
Basavanagudi BMSCE- Autonomous College

Yes, you will get admission in IGNOU, and this university is good for MCA, and it is a good choice for your future.

You can visit directly on IGNOU web page, and can apply there for this course.

There is no fee structure for donation fee for lateral entry in BMS. You can contact college, whether they are giving admission to lateral entry or not, and it is upto them, whether they are taking donations or not.