1) My sim makes garden salad when the welcome wagon arrives. My sims NEVER eat the fruitcake anymore and as soon as their time is up, I have my sim clean up the plate so I don't take any chances of them grabbing a piece. I had no clue that there was a cure till I read this post, LOL
2) I never noticed my sims getting better as they moved up. They always took a citrus bath (think it lasts 8 hours) prior to work to keep them focused. I haven't played it in a while (I love the dr. career though, till I play it too long and they all become ghost, I wish they retired when they got old so it would avoid bringing the reaper to the hospital) but if your sim is not at the level to perform the surgery ones, then you can scratch them off the list of what it can't be. I never spent too much time on one patient. They will come back the next day (I always click them when they are at the front desk first, to see if they have been there) then I just take them straight to x-ray or something else first, then to their bed. Patients are fine sitting in their beds, unlike the ones waiting at the front desk :D So just hop around and get back to that tougher to diagnose patient(s) later.
3) I don't use mods but I do have my sim ask the patient about their day (or any type of conversation) once they are at the bed, then take their temp etc. Your sim will tend to stay there and talk in-between trying to get a diagnosis (at least it helped me to keep my sims from running for coffee or dancing to music) but sometimes I had to queue up for them to talk, so you could try it and see if it helps.