It doesn't save anything, it is just a startup script to get your tmux session set up the way you want. You can however, have env vars in the script or source from a particular file. e.g.
I don't believe it does save env vars. However, as an owner of a crashy 2010 MBP, tmux-resurrect saves my bacon several times a week. I very highly recommend it.
No, but add an autoenv script of your choice, like zsh-autoenv and the combination is nearly perfect.