A few Other World cards refer to closing the gate you entered through. If someone's already closed it, then fine, tough luck, but what about if it's Luke, and it comes up before they've left the Dreamlands the first time?

(It was http://www.arkhamhorrorwiki.com/Image:Gate2.png that came up this time)

I'm guessing "return to Arkham at any Dreamlands gate (or since he'll usually still have the Gate Box, any gate) but don't close it" makes most sense.

Also, is there a clarification yet on whether Find Gate can be used while delayed, or on the same turn as the White Ship is used? (For Luke, as well, can it be used after moving across to the second half, to pick up that extra clue?)

The gate you entered through is just that: the one you entered through. If it's not there anymore for some reason, then you can't close it. Tracking exactly which gate was the one you entered through can be a pain, since it's not ordinarily required by the game. This sounds a lot like a Dark Pharaoh card.

Movement spells may not be used if you are delayed. Using the White Ship or the Nightgaunt's ability immediately ends your movement phase.

Also, using Find Gate is done instead of advancing to the second space of an Other World: you can't do both.