Q: For the card I’ll Be In My Bunk, does it mean that no-one can steal a Keeper, or just that they can’t cheat and look at your cards?

A: It means no-one can steal a Keeper, or a card from your hand, or trade hands with you, or whatever might alter your assets while you’re gone* (but you also would not benefit from Everybody Gets One!). We would consider not looking at someone’s hand to be baseline good sportsmanship, which does not have to be regulated.

“Don’t cheat” is kind of the first rule of every game (unless the game is really outside-the-box, in which case I’d expect it to be very explicit about what kinds of “cheating” are allowed, I guess. And if it’s allowed… is it cheating?)

* Here is a list of the cards in Firefly Fluxx which would not apply to you while you were “In Your Bunk”:
Exchange Keepers
Steal Something
Random Tax
Mix It All Up
Everybody Gets 1
Trash Something
Trade Hands
Use What You Take