I am a spinner because my husband gets on my case if I grind. When I first started riding it was my natural inclination to grind, and boy did my knees let me know it was not a good thing. I think singletrack has it right in that spinning at a higher cadence takes better aerobic fitness than grinding, although on a hill, it doesn't seem to make much difference... I'm still huffing and puffing either way. But spinning really is best for your body. You'll if you get OLN that all those guys in the Tour and the classics spin. Their cadence is always high.

Weights will definitely help. I know BikeGoddess has a whole weight training program that she says has really helped her. Maybe you could PM her and she could give you some help in that area.

As far as what is a hill... I don't know your area and can't really tell you. But around here, if it's a 3 or 4% grade or more and goes on for at least a half mile, I consider it a hill. Anything less than that is rollers to me.

As for the other stuff... I can't help ya. But welcome to TE and have fun riding!! It's great to have you here!