I pulled out my axles today to replace the wheel bearings. It looks like the bearing race seperated from the rest of the bearing and stayed in the axle. It wasn't tight at all and I could pull it out by hand.

So are the bearings supposed to pop apart like that, and do they have to be replaced every time the axles are pulled out?

Sounds normal to me.

Here is another oddity. I go to buy the axle seals and there are different part numbers for both sides. What gives?

IIRC the axle seals are different for each side and non-interchangable.