Bad tires and bad alignment can cause the car to shake at certain speeds.
yes, 65;
You need to check your brakes and rotors. Typically when the rotors go out it will make any car/ truck do that.
Filling your fuel tank will not make your car shake, unless you got some bad fuel that was contaminated with moisture.
I just fixed this problem on my own car, and it was that the rubber part on both the right side motor mounts was broken, so it would shake and make a loud noise when in drive and especially while accelerating. Depending on your car, you might be able to check for yourself, at least on a top side mount.
Nope.
yes, but only when the brakes are applied.
yes
Get the tyres checked for balance, and bulges in the side wall.
Bad engine cushions can make the engine shake. bad spark plugs cause malfunction as the car starts running.
no that would be a mount or a tire or a rim.
Your tie-rod ends or ball joints are probably badly worn. Or it could just be air friction pushing your car to one side.....