You'll have to adapt to the stick too and it can take a while to get used to... The stick is convenient because of the way the buttons are mapped out.
Chances are you'll keep getting your butt kicked at the beginning, but if learn how to use it well enough, the stick can be very accurate for picking the motions you need to pull off some moves.
Pretty much. In other words, the stick won't magically improve your game.
Invest your time in learning how to play the game first and eventually, you're going to know from all the practice and the knowledge of what you're capable of doing in the game whether your current controller is up to the task.
From my experience, a regular Xbox360/PS3 controller wasn't enough for SF4 (IMO, triggers are awkward) so I got a controller with six buttons on the face.