What you are describing as unsettling is due to negative G forces. The object you are in, whether a roller coaster or an airplane, falls away from you at a greater rate than the acceleration of gravity.
But you sound as though you DO like an INCREASE in G forces...which is what happens when you go in loops and turns in a roller coaster, aircraft, or even car.
A helicopter CAN experience both positive and negative G forces...it just depends on how it's flown...same as with an airplane. A "normal" ride in a helo wouldn't thrill you much if it's G forces and speed you like. Helos aren't that fast and don't experience a heck of a lot of G force deviations. (But they ARE fun to ride in IMO!)
If you like speed and +G-forces and want to do it in something that flies...I'd suggest you find an aerobatic pilot who has a two-seater airplane...just tell him not to do any nose overs or hammerhead stalls, or else your stomach will be in your mouth.
generally "No", not like a rollercoaster-unless the tail rotor malfunctions.................
Not at all, it feels like you're hovering over in a seat, which is what you're doing. Think about jumping on a trampoline, and at the peak of your jump you sit in a seat and don't fall. It's a very relaxed and scenic ride.
Depends on the pilot.
On a sightseeing ride, the pilot tries to keep the helicopter flying smooth and level.
You will feel some up and down, but it's really amazing how the blades act like a very wide wing, so that you feel rather stable in the aircraft.
If the pilot wanted to, he/she could follow the terrain very closely and make it feel like you are on a roller coaster. (High rate of climb/descent.) But I don't think most pilots of sightseeing helicopters do that - they would not have many customers returning, or many referrals.