My daughter is 2 years and 3 months. My daughter is alot like yours...she doesnt really sit still unless she is pre-occupied with something. My expecation is for her to sit no more than 7 mins if I am lucky. She will sit longer if the task she is doing is more intersting..I was amazed how much Play Dough lets her sit for over 30 mins while she just plays. I showed her how to create things with the play dough (make a daddy, make a flower etc) and she just makes things out of it...so fun to see their immagination role.
For FOOD...mine is still in her highchair. I give her a new toy for the month. its usually something to do with the month and is one of my old decorations for the house. Right now she is playing shamrock...next month will be a plastic bunny and easter egg. I have had to set a timer for her when I cut her hair. I set the kitchen timer and let her look at it so she can count down. that gives me 3 mins to cut her hair. ...doing her nails is the same way, I use a timer in the kitchen. I Do give her a reward if she sits still through the timer (and then make a BIG deal that she was such a good girl)...anyway bribery has worked for me....
I know when she is at school, they have reading time for 45 mins. All the kids line up along the wall teach reads them stories while they get their morning snack....I dont know how they get all of them to sit that long LOL.
EDIT...for brushing teeth, I bought mine one of those electric ones....she LOVES it and has no problem brushing her own teeth now...They are cheap too...like $7 at the grocery store.