Uttar Pradesh

Of course. But, I think, you have to apply for admission. But currently Spot Counselling is ongoing. Check LU's website to know more.

It is not fake. It is affiliated to CCSU.
http://www.ipseducationmeerut.com/affiliation.html
Check here to confirm. Click on the 2nd PDF.
http://www.ccsuniversity.ac.in/web/Colleges.htm#Prof

MIMS is a very good college and has an amazing environment. Since both the colleges are quite close, you can visit both if you want. HIMS is quite old and a lot of students here practiced medicine in past and are settled somewhere. MIMS is relatively new but is a very good institute nevertheless. I would suggest going for MIMS as a lot of faculty members are the alumni of big institutes.

It's fully dependent on CAT authorities. Maybe, you'll get a centre.

Yes, you can easily get admission. So all the best for future.

Yes, you can. AMU conducts entrance exam for various courses and admission will be based on the performance.

G. L Bajaj has maintained its reputation for last 4-5 years beyond the milestone. The faculty is superb and the institutes main focus is towards the quality education only. For a meritorious and sincere student, it is a heaven. Placement is also very good with 85-90% students getting placed every year.

They will get you placed in any company, just to maintain the record for a number of placed students. But the real scene can just be felt by the students of the college itself. They will help you groom your personality for HR rounds. Also, they will help you to prepare for aptitudes, that is the first stepping stone for every selection process. Several training sessions are arranged to make you aware about the latest technologies in the industrial use. Rest, the job of your interest lies in your hands only. They won't help you get your dream job. They will only get you placed with some or other job offers.
Good luck.

For CSE, GL Bajaj is better in terms of placements.