Any abilities that trigger when the two creatures enter will be put on the stack after the fight, even if one or both creatures die.

If no creatures or only one creature is put onto the battlefield this way, no fight happens.

Players can't cast spells or activate abilities between the creatures being put onto the battlefield and them fighting each other. Notably, you can't respond with a spell like Giant Growth.

Guild Feud has one target: the opponent. You'll see what creature that player puts onto the battlefield before revealing the top three cards of your library and deciding whether to put a creature onto the battlefield yourself.