Hi, 

The eligibility for appearing any entrance requires the candidate to pass there 10+2 boards.

Well if your overall percentage is 66% and individually u have scored 33% in all the subjects(theory+practicals) then yes you definitely can apply for the entrances.

All the best. 

Yes you'll be able to attempt these tests.

According to the guidelines, a candidate must secure minimum 50% marks (GEN), 40%marks (SC/ST/OBC), 45% marks (GEN PH) & 40% marks (SC-PH/ST-PH/OBC-PH) taken together in PCB subjects (aggregate) for NEET and for AIIMS it is 60%.

So it doesn't matter how much you get in an individual subject if your total aggregate is above 60% for AIIMS and 50% for NEET.