If the video camera was on he'd have to ask your permission, and there would (in our surgery) be a notice up about it. Doctors do have to video themselves as part of assessments, so not an indication of anything.
Never heard that about weeing/pooing but never mind...
35 deg is low (I assume it was an in the ear) but not badly so. My dc would be 36.2-36.7 normally.
For checking at that age, I'd expect them to, feel tummy, check temperature, feel the fontella gently and probably check heartbeat/breathing for that. They might also check ears and throat (although that usually upsets the child) and possibly feel under the chin for glands up. I have known one who listens to the tummy, but I think feeling it is more common.
Sometimes they are off food and under the weather for no noticable reason. If she deteriorates (temperature comes up and won't come down with calpol, goes floppy/unresponsive, isn't waking for food, screams non-stop) then go back either to GP or to A&E.
To check temperature by hand the easiest I've found is to put the side of my face against their forehead. Leave it there for a couple of minutes. If their temperature is normal, after a couple of minutes it will feel pleasantly warm/similar to you. If the temperature is up then it will still feel hot.
If she seems happier and better, she probably is. Make sure she keeps drinking, little and often is good, she may take it better by syringe (medicine syringes are great for this) Don't worry too much about the exact amount she's taking, she may not be that hungry. As long as she's taking some and isn't getting dehydrated.
Lots of cuddles-I found like that tucking us both up on the sofa with a duvet round us (me sitting up not lying down) and with something to watch/a book to read, was most soothing -for dc as well as me. In fact ds (age 5yo) still likes to do that when he's ill.