When can I play cards that have a phase listed? For example: challenges, dominance, any phase.

I believe it's only during my turn during that phase, because only "responses" can be played during the other players turn during a phase.

But what about within my turn of the phase? Can I play a "challenges" event, for example, after already commiting my characters for attack and after the opponent has declared defenders? I used a card (I believe it's called Dragon's Fire) this way during a game last night. I commited a dragon (4 STR), my opponent commited 2 defenders (total 6 STR). I then played the event, which is listed as "challenges", to lower the defenders to 4 STR and win the attack.

Am I playing these cards right? Same thing goes for abilities.

tyveil said:

There aren't "other people's turns"; there are player action windows in every phase in which players alternate taking actions. In Marshalling and Challenges, there are certain actions only the "Active" player can take (Marshalling a card, Declaring a challenge).

Challenges/Dominance/Any Phase actions can be taken during any player action window in their respective phase. In your example, there is a player action between Declaring Defenders and Resolving the Challenge, so you can play an event to affect the outcome of the challenge. If you pass to wait to see if your opponent will do anything first, and he passes, then you have both consecutively passed and the player action window closes - you've lost your opportunity to play the event.

To find out more about where the player action windows are in each phase, have a look at the timing flow-charts in the FAQ document.