Accepted my first offer!... thank you email?

Congrats!!

1. Not necessary, but sending thank you notes are a nice thing to do. Let them know you're excited to join the team and work with them
2. I would wait for everything to be signed and finalized before pulling out of the other processes. No reason to worry, but it's probably the prudent to wait. Once done, email your main contact person at the other places and let them know you really appreciate the opportunity/time/consideration but have just accepted another offer elsewhere. They should understand; it's just part of the hiring process
3. Dont think so!