CBSE 12th

Yes you're eligible if you qualify JEE Advanced than you can give AAT exam, center would be the nearest zonal IIT.

Yes you can do B.Sc. with 69.99%.
You are eligible.

Hi,
Admission is based on the marks obtained in qualifying exam. The student needs to score a minimum of 50% in 12th, which you already have.
Regards.

Core field is always in demand rather than IT field. But IT field has more growth, more opportunities. The answer will depend upon you.
If you want core, then electrical will be the best, followed by civil and mechanical.
If you want IT, then CSE, ECE and then EEE/IT.

Hi Aniket, Generally while applying marks of additional subject never counts. Every college is different and hence there admission criteria also varies. Please confirm the university name in which you want to enroll or you can also check the eligibility criteria of the course on their official website. Regards.

Home Science can be included in best four subjects % but they will deduct 2.5%. Or if you opt Bachelor of Science Honours in Home Science then only they will not deduct 2.5%. And every college have different cut off for different course.

It depends on the course that you opted for because every college has a different cut-off for different courses.
You may check the below given link of 2017 cut-off, so you may get some idea of 2018 cut off-
http://www.du.ac.in/du/index.php?page=cut-off-2017

You may enrol in IGNOU.