JEE Main

The cut-off marks as you know vary from caste to caste. Your marks are a very safe zone for backward caste like OBC or SC/ST but if you are a general category student then you might get into trouble to make it into good colleges. If you are a backward caste student, you can easily get Jamia Islamia University or so. You can even check for NITs based on their cut-off last year.

As you haven't mentioned your category, I can't exactly tell you the answer for it. But yes, if you have qualified the cutoff marks then you can get many private college ( you won't get any good government college in this rank) like Jaypee Noida, Shiv Nadar University, Galgotias University or so. But you should keep in mind the placement scenario of the college before taking up admission.

After your Mains rank comes out, they will start shortlisting student out of those who have applied on the basis of their marks and ranking. If you are lucky enough you'll be able to make it into that list and if not, then I am sorry but you cant go into that college.

Yes, you can keep hope for NIT Jaipur. The statistics shows a 70% chance for you to get inside NITs.

Yes, of course, JEE ranks are just for percentage scholarships within 1 Lacs. Above that it all comes down to 12th percentage. I. e. 65% overall with atleast 60% in PCM.

You can't get NIT college with 62 marks. You can try for autonomous colleges and top private colleges.

You can get semi-government or private college only not the best college. For best engineering college, you have to come rank under 10,000 rank or 30,000 rank. So, if you want to try for good marks prepare one year and apply JEE Mains next year.

Your JEE Mains marks is some short but as you said, you are from SC category, you can get a good government or semi government college. If not, then top private college will you get and scholarship from government. Also, I'd provide you the burden of fee will reduce.

No u cant get a seat in NITW unless something big happens.the cutoff rank was way less than urs last year

For JEE Mains, Fees is Rs. 1000.