Engineering Entrance Exam

It depends on your grasping skills. You can prepare using YouTube videos but do take regular tests to evaluate your preparation. I would suggest coaching is better option as they follow a proper schedule and coaching environment encourages individual to take studies seriously.

Hi,
Yes, you can see the answer key of resonance by clicking on this link:
https://www.resonance.ac.in/answer-key-solutions/JEE-Main/2017/jee-main-2017-AnswerKey-Solutions.php

Your rank is around 30-35k and you may get lower NITs or IIITs, but in my opinion apply for LNMIIT and Thapar University as these are better than lower ranked NITs.

This is a myth that state board students are weaker as compared to CBSE and ICSE ones. But the reality is strikingly opposite, in fact people from state board are going for IITs. So, don't get disheartened, prepare for it. As far as the eligibility is concerned you need to be in 20 percentile to get into IITs.

Since your marks in JEE Mains are bit low so you may not get the chance to study in any government college on the basis of your JEE marks. In my opinion start looking forward for your other exams.

Yes, FIITJEE is amongst topmost premiere institutes of India. You can blindly opt it for better outcomes.

Well, you will not get any reputed govt or private colleges. So, better, I suggest you to keep your eye on other entrances examinations. And, if you are quite clear over your concepts, you may put your best efforts in JEE Advanced.
Best of luck.

Kindly clear the college you are seeking for.