Could this be construed as solicitation by a non-licensed individual?

Instead, why don't you just do some mass mailings?  It's going to have the same effect.  The kid can't talk about your business or tell people what  you do.  My personal opinion is that it would look unprofessional unless  you were doing it yourself.  I think instead of asking us what we think, first I'd start with what does your compliance officer think?  Once you have an OK from them, you can come back to us. 

Depends on their age.  if you’re talking high school, no way.  College, maaaaybe.  Early 20’s, could work.  But you should probably set up some formal intern program through your B/D so it’s kosher.