Where do questions go after they are closed?
Are they irretrievably lost? What happens to the rep earned by the asker & answerers.
Closed questions don't actually go anywhere. You can still see them, they can still be searched, and they can be voted back open if people think that they deserve it. Earned reputation is preserved for both the asker and answerers.
Deleted questions, too, aren't really gone either, as they're still visible to moderators and those with over 10k rep, but they're effectively gone as neither the built-in search or Google are able to find them. Though it doesn't happen immediately, reputation gained from deleted questions will be lost when the reputation of all the users is recalculated.
Very rarely questions are completely removed from the system, but I can count on one hand the number of times I'm aware of this happening.
They go to the island of misfit questions where Rich B whips them until they cry. TheTXI rides by occasionally and mocks them from astride his pony, Francesca. Welbog derides the poor usability of the misfit question and we all point and laugh. Shog9 provides them with generally well written joke responses that both flatter and admonish the original poster. Jonathan Sampson will then write a Greasemonkey script to make them appear to be alive again.
Some of them are rescued by a decent edit, but most perish in this hell for eternity. Deletion is too good for them.