It seems that sometimes when I open a replay it repeats the same replay over and over, and other times it cycles through each replay in my folder. I assume I must be pressing some "repeat" button or otherwise toggling this behavior, but I'm not sure how.
I tried a site search using google, but I couldn't find an answer to this question.
Edit: I was also wondering if there are keys for skipping over, restarting, going back, etc, without going back into setup>replays

1.) I don't think there is a key that toggles the cycle of the replays.
2.) The answer to your 2nd question is: Use the "r" button, which will "replay" the replay. I'm not sure about skipping frames of a replay or going back, I don't think there is a feature for that yet.

Ahh, I was referring to skipping to the next or previous replay in the queue.
If there isn't a button to change whether it continues or replays, why is it that sometimes it will only play the one I selected and sometimes it will cycle through?

If you just started toribash, and click on a replay. It cycles

if you click free play , Space, and then click on Replay, it doesn't cycle