We couldn't find this in the rules reference or the quick play. Can you use actions on bowed character cards?

Yes, as long as the cost for said action doesn't involve bowing that card. Its in the rules reference under bow, bowed.

1 hour ago, player1716531 said:

Yes, as long as the cost for said action doesn't involve bowing that card. Its in the rules reference under bow, bowed.

Exactly, as long as you pay its cost (sacrifice a character, pay 1 fate to an unclaimed ring, loose 2 honor, bow this card, etc.) you can use the ability of all cards that are in play regardless of being bowed or not. If you cannot, say bow and already bowed character, then you cannot use their ability.

Also worth knowing, all triggered abilities can be used during any phase as long as there is an action window (or reaction window, as the case may be).

It will be up to the triggered action to tell you other restrictions. These can include abilities that say "during a conflict" or "while you are participating." You can still use those abilities (once per round) if the character is bowed, you are just limited by whatever the restrictions are on that ability. This goes for Strongholds too.

During the Dynasty Phase you cannot play Attachments or Characters from your hand (although you can, as an action, discard 1 unique character from your hand to put 1 fate on another copy of that character already in play). However, you can play Events, and you can trigger abilities already in play (or that you just put in play from 1 of your Provinces). All of these abilities and actions are actions, so you will have to let your opponent go between each action you take and it does make it hard to pass first (and claim the 1 free Fate) if you're doing a whole mess of actions, but you can if want. And I say, "Go nuts!"