Except my friend whose girlfriend, who lives kinda far, goes to the same university as him so she could move to the dorms as soon as the school year started...
"finally" and "at last" are interchangeable, and convey the same feeling of relief. Are we restricted to an approved list of words?
Not on purpose.
It's just that when the course was created, most sentences only have a small subset of the possible range of translations that could occur. Expanding this number of translations per sentence is one reason for the beta period that the course is in.
Please help! When you come across a translation that was rejected because the maintainers hadn't thought of a particular turn of phrase or synonym yet, use the "Report a problem / my translation should be accepted" button (or the one with a flag item). Then you needn't post in the discussion threads, either - reporting is more effective at bringing missing alternatives to the attention of those who can actually make the required changes.
And please be patient. It's a bit difficult to roll out global changes (e.g. "accept large anywhere that currently accepts big") and so in general, changes are on a per-sentence level, so please report every sentence where a given word is not accepted because it wants a synonym, even if you had reported a similar sentence just the previous day.
And changes are not immediate, so it may be a few weeks between reporting a missing translation and that translation being added to that sentence.