CBSE

As for government. Engineering college the candidate must be appeared in respective government Engineering entrance exam. For most of the government. Colleges JEE Mains is sufficient. But some colleges conduct their own entrance exams. Like WBJEE COMEDK etc. Now some private engineering colleges can give admission based on 12th marks. But through JEE Mains you can also get good private college. B.Tech from CSE is top notch branch nowadays so your child has to grind hard to present his skills and get admission in superb college.

It is expected to be out by 3rd August.

Yes, you can easily eligible for the course of B. planning in SPA Delhi.

78percentile is too low to get any of the NITs. You can apply to state engineering colleges of your home state through state counselling. You may get that. Hope this was helpful.

Yes, you can its possible and some of them has done this.

B.Com honours including Maths in (2 year) in the preference of your % criteria these are colleges. Since you have asked for the best colleges let us first have a look at the top ten colleges for commerce in India
SRCC
Lady Sri Ram College for women
Loyola College Chennai
Christ University Bengaluru
St. XavierS College Kolkata
Narsee Monjee College of Commerce and Economics
St. Xaviers college Mumbai
St. Joseph College of Commerce
Hans Raj College
Hindu College.

No, you cannot but you have to choose PCB as subject.

If a candidate has 6 subjects and you failed in 2 subjects then he/she can give a compartment. If a candidate has only 5 subjects and failed in 2 then the candidate is said to be failed.

Yes, you are eligible to apply for St Xavier's College Kolkata