Glad you're enjoying it :D Sending Crow to the tavern is an optional scene where you send Crow to whore herself out. You can unlock it by choosing to get supplies from town at the start of the game, not swapping your shift with Glasha, and then listening to Carmen's offer. At some point, Carmen will ask what you want to do with Crow. Say you're happy to let her play the whore. At the end of the day, Crow will leave for the tavern and you can switch PoV to watch her.
To Poison Carmen you want to not get supplies from town at the start of the game. Lay low, and at the end of the day make sure you feed Carmen on her knees. The next day when Glasha wakes you up, express doubts about the mission. Listen to Carmen's offer, and at the end of the day Roman will pocket something called Red Velum. At the beginning of the third day, choose to finish the mission no matter what.