I've not been able to figure out exactly what the skill associated with each spell does. Does it cause more damage with Flame Dart? Does Dazzle last longer? Etc.
And what about spells like Open, Trigger, and Detect Magic? They seem to always work. I've never encountered a message like, "You're not sure if there's magic here, because your skill is to low."
I guess that also makes me think, is your Magic skill somehow tied to the spell skill?

Magic and Intelligence together determine how much Mana you get. As for stats affecting spells, I think the more noticeable effect comes from grinding up the skill level of the spell itself.

As a rule of thumb...

Damage-dealing (and healing) spells become stronger as the spell skill improves.

Duration-based spells last for longer as the spell skill improves.

For most other spells, spell skill doesn't have an inherent effect, but some specific situations will produce different results based on your spell skill. This mostly comes up in QFG1, where many spell-based actions will only succeed if your skill is above a certain level (typically in the 25-40 range), although it also applies to the Summon Staff spell in the shaman duel in QFG3.