If I'm casting say, a healing spell, will the effectiveness of the spell depend on my Restoration skill? Or does skill only determine the likelihood of casting the spell?

It only affects the chance that will spell will succeed or not.

Thanks. So it's really not a big deal to have a low skill in various magic schools, as long as you don't need to cast those spells quickly. More convenient, but less critical.

Right. Failure at a spell cast in the safety of your home, for example, probably won't anything, but failure to cast a spell you need elsewhere could be dangerous. So it helps to practice--not to mention, you gain the chance to take a higher multiplier on Will or Intelligence (as appropriate) when your character acquires a level while sleeping.