Yes of course if you score really good i.e under 100 (this rank limit very branch wise) then you can get into good PSUs and note this that your overall aggregate in gate is going to decrease as in total your GPA is also included, moreover in the interview you have to face some harsh question due to your backlogs, but if have prepared well for GATE then you can easily swim through technical questions.

Yes you are eligible for PSU's and GATE. But have a very good reason for your year gap or an extra year you took as you will be put through this question in most of the interviews of this domain. GATE just asks for a degree from a recognised university and thats it. Get your technicals very strong and prepare well.

Goodluck