Indian Institute of Technology, Delhi

No way, you need to qualify JEE advance with a very good rank to be eligible.

Sorry to say, but JEE Advanced cutoff for different categories is:
General: 128
OBC: 115
Sc/St: 64
https://www.resonance.ac.in/reso/news/jee-advanced-branch-allotment.aspx
Check this branch and IIT college predictor.

You need a rank under top 500 to get admission in IIT Delhi.
It is one of the top IIT
https://www.resonance.ac.in/reso/news/jee-advanced-branch-allotment.aspx
Check this branch and IIT college predictor,

The admission in any of the IITs is strictly based on the rank secured in JEE advanced examination. If your rank is good, then you can get mechanical engineering at IIT Delhi. If you have not given the JEE Mains and Advanced then you cannot get admission.

The exact numbers are never revealed. But it has to be the lowest among all other branches. Most of the students don't go for core jobs, and most of the students go for higher studies. Remaining students go for consultancy, analyst or coding profiles.

If you are looking for a B.Tech course, you need an AIR under 100. If you are looking for a dual degree course in computer science, an AIR under 200 should suffice.

Some hostels are 50 years old. Some are just 10 years old. No ragging. The mess food is not that bad, but you will eventually get bored of it very soon.

That totally depends on the branch you want. To get computer science, you need an AIR under 200, whereas, you can get textile engineering at around AIR 3000-4000.

There are few companies which come to hire engineering physics students in core profile, Boston, Texas Instruments being some of them. Most of the students actually go for other roles such as coding or analyst and some of the students go for higher studies. Being a student of IIT Delhi myself, I know that students of this branch are not that happy with curriculum and unless they have deep love for physics, the students always try to get out of this world of physics.

IIM-Nagpur is new and will take time to gain reputation and placement . It is better to go for IIT-Delhi.