I don't think a tie would hurt. In most cases though I would say a professional looking button down shirt tucked in and a jacket with slacks would be the best approach.
I just received notice that I got accepted into my third choice. I am now waiting on 1 and 2. Should I e-mail the professors from 1 and 2 expressing my interest and asking for an update on the status of my application and reiterate my interest in studying with them?