Please note that this thread is intended as a place to collect official answers to rules questions, not to ask questions.
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Regarding your questions:
1) The ability affects both players and requires them to sacrifice a character whenever they draw one or more cards in a draw phase. Please note that sacrificing is a different effect than either discarding or destroying. The underlying theme of the Cthulhu faction is sacrifice/destruction and it's beneficial to play Cthulhu whenever you have either have more characters in play than your opponent or weaker characters. It also has a general effect of creating a board position that is easier to analyze because there are fewer characters to take into account.
2) This is not an uncommon situation if you're playing with the core set only. It's less likely to occur in games with carefully created decks, but it can happen. There's no limit to the number of characters that can be in play at the same time. As indicated above, Cthulhu is one of the cards that can help to get rid of excessive characters.
3) The keyword 'Loyal' indicates a card that can only be played if the domain drained to pay for the card's cost contains at least a number of cards of the card's faction equal to its cost. In addition there are cards with a Steadfast requirement indicated by small faction icons in front of the card's title. THese cards can only be played if you have a number of cards of the indicated faction among any of your domains.
