Do illusion spells work on dragons

What does this mean?

It means, you can take out your completely empty Sword of Flaming Flames, kill a bear with it, and now it's got 5% of the bear's soul for the next fight. (note: works for partially filled magic items too)

Does this require you to have an unused soul gem in inventory for it to work

Nope.

and how does it interact with a soul trap weapon?

1. The soul trap weapon casts soul trap on the creature.
2. The creature dies.
3. 5% of the creature's soul is stored to the weapon.
4. 100% of the creature's soul is stored to an empty gem.

Yes, that is 105% of the soul, which is awesome.

Mage armor only affects the duration spells under the alteration tree. The ward spells add their stated value to your armor rating, but this will not negate the bonus from mage armor. So if you have max mage armor that multiplies ebonyflesh by 3x, and then you cast a ward that gives you another 80 armor, then your character will have 380 armor.