The only thing I could probably give you advice on is feet, bladders and teeth.
I rest their backs against my belly while sitting down, kind of put their butt on my lap, and gently hold them with one hand and use the other hand to get their paws. I check their feet, toes, and between their toes for rough areas, extra growth, or sores. If I find extra growth like spurs, I cut it off with the toenail clippers. If I find rough areas, I use a little bit of aloe.
For teeth, I roll them onto their back and spread their little cheeks to make sure none are broken or have anything stuck in there. I usually can only see the front teeth though, I don't know how to check the rest of their mouths.
For their bladders, to check for stones and the like, I sit them right side up again and put my fingers on either side, move them back towards their butt till you feel a balloon like thing- that's the bladder. Gently palpate it and feel for any hard spots.
Anyone, please feel free to let me know if any of this is misinformation.