B.Tech

Yes. You can give a try. According to first counselling list of thapar, 60 score can get you in your 2-3rd preferred branch. But undoubtedly, you can get admission in thapar. Visit: www.thapar.edu.

Electronics from NIT (J). Look, first of all NIT has more reputation than thapar. Though Teaching of thapar is more better than NIT, but Thapar's standard is decreasing day by day. Plus, fees gap between two is so high!
I would suggest, NITJ.

Yes! Undoubtedly. Last year, at the end admissions were made open. Means, if a student hasn't filled thapar form, he/she can get admission in vacant branches. So, yes. Ofcourse. You can take admission. You don't need to wait for last round. You will get before that as per first counselling list. Visit www.thapar.edu for more information. Regards.

Government colleges have more reputation than private colleges. But if you are looking for good placement, then some government colleges don't provide good placements (not all of them).
And there is also mass recruitment in all colleges. So you have to be unique if you want a good package. UPES provides good placements. But mass recruitment is also present in UPES.
VM provided more than 15 LPA. Microsoft gave an offer of 11 LPA.

Hello,
I hope you are doing well. You can check the list of colleges including NITs and IIITs that you can get according to your marks and rank. Use Shiksha JEE college predictor:
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor?utm_source=connect&utm_medium=CR_JEECP&utm_campaign=7489993.

You can apply for counselling based on your 12th marks. Or else, apply for JoSAA counselling based on your JEE marks.

It totally depends on the college.
In government colleges, it ranges from 15k to 70k.
In private colleges, it ranges from 70k to 300k.
In NIT, it is up to 1,20,000 and in IIT, it is 2,00,000 (tution fee, excluding accommodation fee).