I'm trying to do the Bloodwing Hunt, but I can't teleport into the Barheim Passage for some reason (It's just not on the teleport list). Is there any other way for me to get in? One entrance is blocked and the other is locked.

Complete the Dalmascan Patient sidequest and you will get the Barheim Key and be able to unlock the door.

The save crystal in there becomes a Gate Crystal once you get the key. Visit it once and you can use it.

i have the barheim key, but the save crystal is still not accessible when i try to teleport.

You have to use the key to get in instead of teleporting. If you want to teleport the only telport crystal is only accessible once you go back into barheim, not when you go in for the first time. Also, you need to touch it before it will be on the teleport menu. If you have done those things and it is still not there then either i can't help you out or something is wrong with your game. Good luck with bloodwing.

The first time you go through the barheim passage it is much more fun to do it with the lights off. Then you get spectres and zombies and you level up more. It's also more challenging and therefore in my opinion, more fun.

I think you'll need the Barheim key, which was explained above in the Patient in the Desert quest. Now that I think of it I don't think I was able to teleport in and out of there before I got the key. I ran into Bloodwing on accident though so haha

The reason that it changes from a save crystal to a teleport one is cos square want you to go through the quest of helping the people in the estersand rather than just teleporting back into barheim whenever you want too.