GATE

Hello Shubham,
There are few vacancies every year due to shortage of admissions in various engineering colleges across the country. The institutes also releases notification for admission into such seats by non-gate candidates.
I suggest you to search for such institutes as these seats are less in number.

If you're serious about cracking GATE, then start taking your major subjects of CASE seriously. The ideal time to start preparing for GATE is from 3rd year and as you're in college it will be quite difficult to do self-study as you also have to manage your Graduation studies. So, it is good to join a offline coaching class where you will get a mentor to guide you through out your journey. Mostly, all coaching centres provide weekend classes which can be manageable with your college.
Good luck.

Yes. But, it requires four years after 10+2. So, you have to pursue your M.Sc degree.

Thapar University expected cut off is obviously less than IITs and NITs but not that much less. It would safely be upto GATE score of 450 to 500 and above. There is a separate entrance exam if all seats are not filled through GATE.
You should apply for that.
Best wishes

Yes, candidates who have completed their engineering (even in 5-years) are eligible to pursue GATE exam. Please refer to the link provided below for detailed eligibility criteria where you can check for your eligibility to appear for the GATE exams. https://www.shiksha.com/engineering/exams/gate.