Engineering Entrance Exam

No, you cannot appear for BCA after GATE.

No college would submit your any of the original mark sheets. They would ask for the migration and TC certificates originals which you can easily get from the school or board by stating it to be missing or any other reasons. All the best for your preparation.

If you feel like working for core companies and have a desire to work for a better organization rather than crawling in those MNCs, then drop a year and do preparation for GATE.

This is according to the GATE 2017, negative marking will be only for the multiple choice questions (MCQs). For 1-mark multiple choice questions, 1/3 mark will be deducted for a wrong answer. Likewise, for 2-mark multiple choice questions, 2/3 mark will be deducted for a wrong answer. There will be no negative marking for a wrong answer in numerical answer type questions.

Sorry, it is not possible. Your marks are too low. You have to score around 120 marks in JEE in general category to get a good stream.

Hey, have you applied for admission through sports quota? (you have to fill a separate admission form for this)

Yes, it's compulsory to score 75% for general category students and for SC/ST, it is 65%.
All the best.

Only if you do good in mains as well as scored minimum 75% for general and 65% under ST/SC category.
So, you need to work hard for another year.
And you have to appear in Mains and scored a good rank accordingly.

No, they take admission through MHTCET exam conducted by Maharashtra government but if some seats are left then they can take admission through JEE Mains marks.

Check the college which you can get by your rank, category and branch specified by the link provided:
https://www.shiksha.com/b-tech/resources/wbjee-college-predictor