"I walk down the hallway."
Is that specifically for "down" the hallway? What about up the hallway, or just saying the hallway?
I don't think Japanese makes the distinction between walking up or down the hallway. 廊下 is simply "the hallway" and the directionality comes from the particle を to mean "through", as opposed to 廊下に "to the hallway" or 廊下で "in the hallway".
In the last lecture we had o for bridge. Is there also a de version for it?
Yep, を is right. It's a bit of a weird quirk with the way movement verbs interact with particles. I'm not a grammar expert, but I'll try to explain why.
Other particles commonly used with movement, に (or へ) and で, subtly don't work the way you might think. As I mentioned in a previous comment, 廊下に becomes "to the hallway" and 廊下で becomes "in the hallway". This is because に indicates the target of your movement, and で indicates the location, but not the direction, of your movement. Using で implies that the action takes place only at that location, and not necessarily to enter or exit the location.
By using を, the direct object particle, with intransitive movement verbs, the notion of "subject + verb" is applied to the location as a whole. So, the idea of "I walk" gets applied to "the hallway"; the only reasonable interpretation of "I walk the hallway" is that I am walking through the hallway, be it going up or down.
Other common examples of を + movement verb include:
曲(ま)がってください "Please turn right at the next corner"
渡(わた)っていけません "You must not cross a red (traffic) light"
通(とお)ります"The highway passes through the mountains"