Several questions, and I think each one is a little different.

1. Ser Jaime Lannister (Valyrian) : "At the beginning of each phase, stand Ser Jaime Lannister."

... would this mean that Jaime stands up at the beginning of the Dominance phase, and his strength is counted to determine the winner of Dominance?

Is that a "passive" effect, or a triggered effect, or something else?

2. Court Archivist (Valyrian): "Dominance: kneel Court Archivist to draw a card."

... if I remember right, player actions come after you determine the winner of Dominance. So you would count the Archivist's strength to determine the winner of Dominance. And you can still kneel him afterwards to get a card.

3. Firemage and Eviscerate (Valyrian) ... almost the same kind of effect:

"Dominance: kneel Firemage and kneel 1 influence to choose a character without attachments. Until the end of the phase, that character gets -1 STR and is killed if its STR is 0."

"Dominance: kneel 1 influence to choose a character without attachments. Until the end of the phase, that character gets -2 STR and is killed if its STR is 0."

3a. Again, since player actions come after determining the winner of Dominance, Firemage's STR is counted for Dominance?

3b. Again, since player actions come after determining the winner of Dominance, the target of the effects don't suffer a STR penalty when the str for Dominance is being tallied.

Stormtower said:

1. Jaime's ability is a passive effect. It occurs during the "Dominance phase begins" action window (see the FAQ flow charts). The Dominance account is in the next framework action window so Jaime's strength will be counted for dominance (barring other effects of course).

2. Yes. Again, look at the flow chart in the FAQ. Player actions occur after the dominance count framework action window.

3. a. and b. Yes and yes.

Stormtower: I really suggest you read the FAQ (or read it again since your understanding of phase timing is good and no doubt comes from there). A bunch of your recent questions have all had direct answers in the FAQ - general answers as opposed to card specific, but all in there.

Thanks for all the responses!

Yeah, I finally found a copy of the Legacy FAQ as well, so questions about the old CCG cards were clarified in there.