GATE

Yes, GATE is quite important exam as a good score not only ensures your admission in IITs but also gives you a chance to get into PSUs.

You can try Thapar Institute of Engineering & Technology. First, preference is given to GATE qualifiers but after that vacant seats are filled by students who haven't appeared GATE as well. Plus, you have experience so that would give you an edge.

Yes, you may apply for admission on the basis of graduation's percentage. Some good universities conduct their own entrance exam so, you can apply for the same. Some good universities are Christ University, Lovely Professional University, DTU, Anna University, Jadavpur University.

In every engineering sector you have to give GATE for pursuing higher qualifications or for getting a good job.

10 Expert Tips To Crack GATE are mentioned at the link provided below:
https://www.shiksha.com/engineering/articles/10-expert-tips-to-crack-gate-2016-blogId-11497.