in the rules of the Full Game category, it says you may die in the arena, but the arena must be restarted. does this mean restarting from challenge I or just restarting the level you were on? and also, are deaths allowed on any other part of the run?

Sorry for any confusion - The rules just mean you have to restart the challenge itself, not that all the arenas have to be replayed (just got to finish each one once, however that happens).

The time taken on a failed arena runthrough will still be added to the final time however. For example, if you finish Beneath first, then finish Arena 1, then start Arena 2 and die, you have to restart Arena 2 and beat it at some point during the run for it to count. The rule is just there to be clear that dying in one of the Arena challenges does not mean you've 'completed' it.