When I part ways with a follower, do they teleport home once they are out of my current area? Or do they walk the whole way?

I don't want to dismiss a follower who has some of my good stuff, only to find out much later that they were killed somewhere while walking halfway across Skyrim to return home.

nope they walk, but never had one die yet. I think once they get dismissed they become immortal I followed Lydia once (from a respectful distance) she walked all the way back and did fight a few wolves and a sabre cat on the way back. handled her self just fine

Followers can only be killed by the player.

Not true. However, they typically yield when at low HPs, which means the enemy attacking them will most often move on to another target (usually the player). But if they take enough damage in one hit, or otherwise don't get a chance to yield, then they can be killed in a fight by your enemies. Seen that happen many times (to my wife) - all you can do is loot the body.
I'm even pretty sure I had Lydia get killed by a TRAP one time, but I could not find her body, so maybe she just got lost or there was a glitch that made her go invisible / teleport away / cease to exist.

Yep, I've had followers killed by both traps and enemies. As you mention, if there is another target, then the enemy may shift to them. But when returning home, the follower will be all alone. So I wasn't sure if I ought to bring my follower to near their home location before parting ways.

I think I'll play it on the safe side for now, and when the CK comes out, I'll investigate how that action actually works.

poison is a followers worse enemy. because even though the enemy stops fighting them, the poison kills them in one tick.

They walk. I once dismissed Lydia in Windhelm, messed around for a while, headed towards Dawnstar and she was walking down the road FROM Dawnstar towards Whiterun. Apparently she had taken the long way to get back home.

yup, they walk back home.

they can die the same ways that the player can.

This. I had Mjoll pick up Hjalti's Sword so I could find her when I wanted to (activate the quest, look for the arrow). I kept jumping into map mode to find the arrow and it slowly moved across the map.

They musy walk pretty slow - I started the Companions 1st quest with Farkas (sp?) which caused Lydia to be dismissed in Whiterun. I went to Dustmans Crypt, did the quest, back to Whiterun - no Lydia in palace, in companions hall, or in my house! Even walked around Whiterun for awhile looking

wtf???