Even on the grand finale night, are आप allowed to vote that night?

Yes. Why would आप think different?
They (technically, its just Ryan, but still) give आप numbers for the two finalists and then आप vote for them. Most of the time they will give आप three numbers a person, to keep the lines open. आप do 186643657 and then what ever number your vote is.

What do आप mean द्वारा grand finale? The very last show? Because आप can't vote then.

i actually dont know but i think आप can but only for only when it comes to grand finals of american idol ae