Hello harshit

IITB is top level college so your preparation should also match that level . Coaching might give you a bit help but without coaching is also completely fine ,infact I feel it is better .First take a print out of the syllabus and carry it with you .Try completing the theoretical portion then attempt a lot of question on that topic .Previous year questions is a must .Then buy some test series (it really helps a lot ) .There is no hard fast time table for preparation ,you can make your own as per your need .

For eligibility of gate exam check out this

https://www.google.com/amp/s/engineering.careers360.com/articles/gate-eligibility-criteria/amp

Best wishes