Doctor career

Oh, that is nothing, the clinic must have doctors while you are on the lot, it will first try to pull them from the non played sims, and than played sims same as patients nurse and intern. If there are two doctors in same household one will be active and the other one will be inactive. It takes the npc charactors a while to come home from the doctor career and the patients a a while to give the allusion that the clinic is very busy as you arrive the next day the people that where working the previous shift leaves the hospital. Also this allows the clinic to be staffed incase a pregnacy happens whether it is player controled or npc controled. I don't know about the connection thing on the desk of the clinic I never seen it before, but from time to time you can click on the desk when you are at the highest level to trait outbreaks outside the clinic, or cure a sim that is too sick to make it to the clinic. The clinic is a 24/7 medical ward and not really a hospital.

Edit: if you load a sim up and they appear at the hospital if they don't have the job duties ui on you can send them home. I always find some kids in my playable families stuck in the hospital when I load up another family. I just click on home icon and send them home, if you don't get that its a bug.