If you have marks above the cut off for the JEE ADVANCED, then you can give the advance for getting selected in top IIT'S, but if by chance you didn't make into IIT'S, Then by God grace you have already cleared JEE MAINS, and you will get any NIT'S, upon your AIR rank.

If you are talking about JEE main then for IIT you have to another exam JEE advance.

If you are talking talking about jee main for b tech admission you get direct admission if you score above required IIT cut off.
If you are talking about mtech through gate, then in some courses you have to give tests and interview while for some there is direct admission.

No,after passing the cutoff you are eligible for the admission if you successfully get the seat.

No, if u clear the cutoff of respective branch u can get the admission in iit.