1. Roads are fine for touring bike.
2. It's about a half mile to hang site. There are some logs you would have to lift your bike over. You'd have to push it along rocky trail. You could get it there. Push up short steep hill right before hang site. Not a breeze, but doable, IMO.
3. I don't know of any secure areas. You may want to contact park service about that. There's a museum and other buildings there where you could stash bike if Park Service allowed. You'd have to make arrangements with them.