Most of the side quests that I found were depending on certain times in the day/night but not during the missions. After dealing with the hospital I went back in to find a sidequest on talking to the nurse. I'm still in this first chapter on the next day so I've not gotten that far ahead past seeing what happens around 4am in the game, good time to go out for a drive around town to fish or do the driving minigames.
Believe that as you're crouched down that you are holding your breath hence the near heart attack. Just found out today while playing that after hitting a few lightpoles with the car that there was a bill in the sherrif's desk that had some bills but you do get $ in the game for shaving, cleaning your suits, checking in daily, etc.