Is it necessary to have advance reservations for anything in Siena? The Duomo, Baptistry, etc.?
No. Easy.
Janis, I don't recall any problems getting tickets for the Duomo or Baptistery in Siena, but for visiting the Duomo you'll need to be very careful with your clothing choices! On my last visit there, I witnessed a group of University students touring the Church, one of whom was wearing a sleeveless T-shirt. He wasn't allowed inside until he donned a paper tablecloth, with a hole in the centre for his head. Of course, this was an excuse for merciless and never ending teasing by his friends. Happy travels!