As I get more skill points, I've noticed I have more than 8 active skills. Can I actually use more than 8 in combat, or do I need to respec and get a little more focused with my skill point distribution?
No, you can only use 8 active skills at a time. You could keep a couple of extras, and swap them around between battles, but I would not recommend it.
As you say, I'd recommend a respec and focus your skills a little more. I often found that going for 1 tree mainly, along with a secondary and the specialization worked the best. For example, my mage is a Fire/Spirit Knight Enchanter, with points mostly focused in Fire.
Focusing on certain skills like this will make the individual skills much more powerful.
On a side note: if your companions have more than 8 skills, they will actually use them if the AI is controlling them, provided the skills are enabled through the tactics window.