Jabalpur

I think you may directly contact that college. They offer you admission on the basis of good academic performance in class 12th class and they also require valid JEE Mains score.
Check our JEE Mains college predictor:
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor?utm_source=connect&utm_medium=CR_JEECP&utm_campaign=4067795

IIIT-Jabalpur takes admission through JEE Mains, so if you are eligible for JEE Mains, you are eligible for IIIT-Jabalpur. See the eligibility criteria on information brochure provided by JEE Mains at their website. You need to score 60% and above in 10+2.

Fees for BE in Jabalpur Engineering College is less.
Fee in every branch is Rs.11.3k per semester.
If you want to live in boy's hostel or girl's hostel, fee is Rs.1300/ year without mess.
And, semester examination fees is Rs.1300/per semester.

Closing rank for OBC category in JEE Mains of this college for (given rank may vary 2-3k):
Mechanical Engineering-70k
CSE- 72k
Civil Engineering - 75k
Electrical Engineering -75k
EC - 90k
Information technology- 95k
Industrial and production- 110k
All the closing rank is up to last counseling.

Infrastructure of GGITS is better than SITS. But, the fee in Shree Ram Group is less than Gyan Ganga College. But, placements are approximately same in both college.
For more details you can visit:
https://www.shiksha.com/resources/college-comparison.

Yes, you can apply in Jabalpur Engineering College for BE (lateral entry) with CGPA of 7.99. Because, my friend is also pursuing BE in Jabalpur Engineering College with 6.5 CGPA. Hence, you will get JEC, Jabalpur easily.

There are lot of technical and cultural event organised every year for example-
Aureole, Alumiae meets, sport fest AAVAHAN, spots fest VNMCT (ONLY FOR BOYS HOSTELS), PRAPANCH open fest etc.

You cannot do as UGC itself and ang universities do not allow the same. also there is no point on doing 2 PG together as per new CBCS scheme many universities allow you to pursue a PG degree of your choice and you can choose subject from other specialisation.