Yes.  If you were a professional dancer, you wouldn't think twice about it.

> Secondly, on occasion, one or two of the girls will get a little too close to > me than I am used to (since I am not REAL used to children). Sometimes they > like to hug me, or they like to sit on my lap with their arm around my neck. > Is this normal... or if it's not, how do I get a kid to stop this without them > feeling like I'm pushing them away?

Yes it's normal.  Dancers can be a very physical lot.  Best way to stop it is to not respond to it.  Or speak with the girls.  You should set boundaries you are comfortable with.

> Also, how would a parent react to their child exhibiting this behavior around > me or seeing a late-thirties male lifting their daughter??

Lifting is expected in ballet, dancers understand it to have no romantic connotations in real life.  You lift one girl, you lift the next, you lift when and how you're told.

And lastly, of course: never, ever, ever allow yourself to be alone with one of these kids.  Stay in public in the studio.  Safeguard your own privacy (i.e. the sanctity of the men's dressing room).  If you follow these cardinal rules, you'll be fine.