Helicopter rides aren't available between the islands. Since the guy there doesn't really speak English, I didn't understand whether it was because it was off season or it just doesn't fly anymore. (I did see the helicopter a few times while I was there, though.)
Seaplane is available for tourists and it costs 4100 rupees. You can only bring 5 kg of luggage with you or pay 97 rupees per kilo for excess luggage. (Side info - I tried sending my luggage by Makruz catamaran but they didn't want to take it if there was no passenger accompanying it.) Times of departure are not fixed but the seaplane leaves Havelock approximately at 8:00 and 13:00 every day.
I don't know about the schedule for other destinations and routes but since this one matches the one from the official website, I imagine that other info is correct there as well.
It takes around half an hour to get to Port Blair and the view from the plane is amazing.
You book your flight in Village No. 1 half an hour before the departure. One unfortunate thing is that you can't take photographs from the plane or film the flight.