Engineering

All 4 years' syllabus is mandatory for all branches GATE examination. Mostly you should prefer for Maths of 1st and 2nd year for the better scores.

All the colleges in India contains few seats for JEE Mains student may be mostly preferred private colleges can give admission through JEE Mains marks.

Yes, there are various types of MCQ pattern tests in India all over various states which score can get us into the local government colleges in that particular state
For. Ex Maharashtra has- MHT CET exam, etc.

For IIT Hyderabad, the minimum cutoff for JEE Advance might be around AIR 600. For more information you can also contact to the college website once.

The cutoff list for latest spce was about 97 around for spot rounds for core branches and for tech might be 98 or 98.5 some what in spot (means 3 Rd round)

Here is the list of few colleges
1. University of Mumbai
2. Padmashree D. Y patil Vidyapeeth
3. Amity University
4. St. Xavier's College
5. IIT Bombay.

The candidate need to have a minimum 55% in 10+2 from any stream with mathematics. However, the cutoff may vary depending upon difficulty of exam.

Yes, you can change branches but there are some criteria that you need to fulfill for branch change.
1- You must have cleared your first and second semesters with no backlogs or must clear your first year without a year back.
2- Your CGPA must be 8 or above 8.5 on a scale of 10.
3- You have to check in IoT or Data Science branch must have vacant seats else it is not possible.
4- The first thing you should talk to the HOD of the branch you want to go in and secondly get in touch with the college management on this issue.
I hope this will help you.

GATE open many doors for you like in ISRO, State University, corporate sector. And Ph.D. is always available for you. There are many jobs which have minimum eligibility as GATE qualification.