JEE Main

I'll prefer you to join any other coaching institute like Allen and Resonance as the coaching institute mentioned by you is also quite good. But the main problem is that their passing ratio is not that good.

The eligibility criteria for JEE Mains counselling is to just appear for the JEE Mains paper, whether you have qualified the exam or not.
You are eligible for the counselling, but yes, if you haven't secured 75% marks in the boards exams, then you are not eligible for admission in any of the colleges through Mains counselling.

Yes, it's hard as JEE Main but not as hard as JEE Advanced. If you want to crack this, you have to clear your all concepts of 11th & 12th standard.

For getting admission in an engineering college, you have to apply for JEE exam. If your JEE Mains score is low, you can get a low NIT, but there are less chance for you to get a good NIT. Apart from this, you can get good government colleges in your area. To get admission in those there is a different counselling form for every state.

You have to secure under 7500 rank. Only then, you will be able to get the admission in the main campus with CSE branch.

You have very less chances of getting a government college. With this rank, you can get some of the good private colleges, but getting any government college is very difficult, if you are from general or OBC category.

Yes, you can get a government college with this score, but in the central government colleges, there is no defense quota.

Not unique, as there are 4 sets of question paper. In these papers, all the questions remains the same but the sequence changes.

Allen is the best institute for the IIT-JEE preparation, and I'll suggest you to opt for the hostel, if you are residing in home, there is no study environment, and so you can't be able to give your best for your paper.

Colleges have seats for Management Quota also, so you can visit colleges of your interest for discussion, but highly reputed college might not give admission. But, if your ward is serious about doing B.Tech in CSE, then it is not necessary to study in highly reputed college.