IIT

Your CRL rank must be 2000-5000 to grab a good IIT with mechanical branch.

Yes, if you qualify GATE with good score.

both are good courses.But in India there are a few colleges which provide bs research.

You should firstly work on clearing your basics.

12th board percentage will not be included but a certain percentage will be set as cutoff( for CBSE it's75%) and those getting below will not be able to write the examination.

You cannot take admission in IITs by LEET.

Different IITs have different area of engineering specialisation. You may visit https://Shiksha.com portal for ranking of various IITs branch wise.

Here are some tips which you can keep in mind while preparing for GATE :
Go through latest syllabus of GATE.Make proper plan of what you have to study.Read articles written by previously qualified candidates.
For more tips check this link out:
https://edudrona.com/questions/question/how-should-i-prepare-for-gate-2017

You must go for Roorkee college of engineering Roorkee. This college providing you 4 years B.tech course in different fields like petroleum engineering, Mechanical engineering, Automobile engineering, Electrical and electronics engineering, Electronics and communication engineering, Civil engineering. Rce roorkee got best placement award since 2 years by indian government. you can visit to www.rcerooekee.in or contact 7500108111.