Yes, you can spin worsted on a 2.2. You can also spin any size singles and ply together later to make the weight you want.
No you don't need a lighter spindle for spinning fingering or DK. A lighter spindle would be used if you are spinning finer fibers.
The spindle weight is the spindle as a whole.
You can do either with the roving. I would at least predraft it by pulling it open some, as I get better control that way.
Sounds like you are really getting the hang of it there!