How many moon cards can some play in a single round/turn/combat? And to follow that, do the moon cards that let you re-roll certain symbols let you re-roll your opponents dice or just your own?

Thanks for any help!

You can play as many as you want in any situation they are aplicable. You still can't reroll a die more than once, still.

Some of the cards can force opponent rerolls as well. It depends on the specific card's wording.

If the wording doesn't specify who re-rolls, can you use that to make them re-roll? I'm thinking of cards like Suinij's depths which says: After a roll is made, play this card to re-roll a fire result.

Yes. Unless it specifies, like "friendly ninja" or "opposing player" or something like that, you can use it on anything that fits the bill. The ones that re-roll a specific die results (from memory here) can be used to force opponent re-rolls as well.

Thanks for the help!