What does this icon mean? Some units have it next to their character model in the party interface.

AOW1 by the way

How do you gain experience? I thought it was just regular experience (i.e kill an enemy, receive 5 exp points. Now you have 5/10 exp, when you get 5 more you will level up).

If so, that doesn't explain why level 1 units have a silver medal :S

Oh also, in the structure interface, next to the gold icon, what does the little yellow air plane icon mean?

A unit gains experience points proprtional to the tier of a unit it just killed. So if you kill a tier 4 unit you get more xp than for killing a tier 1 unit. A unit's tier is determined by the level of the city needed to produce it. Once a unit has gained enough experience points it "levels up" represented by a medal. Gold medals represent the apex of experience for a unit.

I believe that gold arrow you are referring to represents the city's level.

"Fresh" units with a silver medal? Sounds like you built a Shrine of War. That promotes all units to veteran status.

There are no shrines of war in AoW1, but there is a lvl 4 fire spell called warmonger that you can cast that allows new units to be created with veteran status.