I have a question regarding what cards you can look at during the course of play separate from a card effect. Can I look through my domains and the opponent's domain? Can I look through my discard and an opponent's discard?

Thanks for your response.

Yup you can look at cards on domains freely, same with discard pile.

Because resources are public information, to speed things up during tournaments we have players say the title of a card as it's resourced. I now try to make it a habit during all of my games.

I personaly also started to place my resorces title visible and make my discard cards not stacked directly on top of each other but next one below other ones so that title is seen. It helps me check what exactly have i already resourced and what can i recurr from discard.

Many players probably remember this, but i personaly hate memory/percevtivity element in games and prefer public information displayed in as convinient way as possible.