1)Progress in Story you will unlock quests brothel is one of them. Enterance is same area with fight club.
2) To unlock hospital you need progress in Story as well.
3) Trades starts when you enter Strombrad. I am not sure if I remember all of them. I will write the ones I remember. First guy you talked in strombrad, right bottom of Strombrad in WC, Middle of Strombrad a child, top left of Strombrad a man in bed, in fight club, middle right of Strombrad in house with blue roof ( There wasn't trade sign on top of this guy), lastly hospital.