Colleges in Jabalpur

You can get admission over there. Even though the score is less. Some private campuses won't look into it. They will see whether you have attended the JEE exam. Go through the below link to get more details of other colleges which you can apply:
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor?utm_source=connect&utm_medium=CR_JEECP&utm_campaign=4479470.

Yes, you are eligible to get admission in JEC but you will have to crack CEE.

Visit the college which you want to. Get details of your admission, check the fee and take the admission if you want to take. But it is via management quota.

Yes, you can do mechanical Engineering but I prefer you to go with aeronautical because there are lots of scope in it.

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 get admission in Jabalpur Engineering College for B.Tech through lateral entry.
Approx. you need to have 60% or above in your Diploma then you can get it easily.
I would suggest you to before taking admission for B.Tech in any college please you learn integration, differentiation and ITS applications in 12th class mathematics because most of the time lateral entry student suffer due to class 12th maths.

Yes, you may get admission after completing 3 years of Diploma in engineering, you are eligible for taking admission in the 2nd year of BE (Bachelor of Engineering) and B.Tech (Bachelor of Technology).
Best of luck.