1. No, you were not petty, although in hindsight, I guess it wasn't the best solution. A coworker should not be bossing you around about turning the lights on or off. In the future, just go to a manager instead of interacting with her directly.
2. No, she is overstepping her bounds. She is a coworker, not your supervisor.
3. Just keep acting professional. Participate in group discussions. If she bows out, that's her problem. If she starts criticizing what you are doing, tell her that you are doing your job the way your manager asked you to and that she needs to go to them if she has a problem with you.

If you have a manager you trust, I might ask them for tips on how to deal with this person. It sounds like you aren't the only one she has an attitude problem with, so maybe someone needs to talk to her.