JEE

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.

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.

Hi,
Super 30 is an initiative of Anand Kumar in Bihar, to train 30 students every year for writing the joint entrance examination for admission into the Indian Institutes of Technology. Other state students can fill the form and take admission in super 30. You can fill the online form and then send it with a demand draft of INR 60 to this address:
Ramanujan School of Mathematics,
Shanti Kutir, Chandpur Bela, Patna- 800001.

Yes. You may wait until the last round.

You can appear for JEE advance for only 2 times.

You can see the answer key of many coaching institutions released this day evening.
Here is a link for an online answer key by resonance:
https://www.resonance.ac.in/answer-key-solutions/JEE-Main/2017/jee-main-2017-AnswerKey-Solutions.php

First go for NCERT books of physics, chemistry and mathematics. Then go for NCERT exemplar books. After you have completed the both, go for D.C. Panday for physics and Arihant Publication's 8000+ MCQ for both maths and chemistry.

For VJTI, you need to score around 150-160 marks in MHT-CET to get any good branch.

If you have confidence that you could prepare well and qualify for SAT and JEE as well with good scores, only then choose dropping a year as if you don't get desired results after an year you'll be frustrated. So think wisely before you make a decision. Or else, there are many good private colleges as well where you can take admission.