1) How far is a wireless range?
As far as it goes.

2) Can I receive any wireless signal in my dorm room? My dorm is located on top of a hill about 20-40 meter away from the lounge with some obstruction of classrooms and some trees. My room's window facing our classroom building.

Maybe. Try it.

3) What gears to buy if I attempt to connect the wireless from my room?

A wifi card and maybe get one you can look at freeantennas.com for ideas how to boost the reception.

These are not joke answers. Wifi and radio does not drop dead at so many feet.