It's not possible to disable compositing in elementary OS. If you feel like you need to disable compositing, your computer is probably much too old to be running elementary OS.
Disabling animations could have some impact on performance.
You can disable window animations under System Settings > Universal Access > General. This includes the animations for opening, close, and resizing windows.
You can disable in-app animations through
gsettings with the Terminal command:
gsettings set org.gnome.desktop.interface enable-animations false
You can re-enable in-app animations by setting the key to
true instead of
gsettings set org.gnome.desktop.interface enable-animations true
Bear in mind that in-app animations are not exposed in System Settings because it may cause undesirable behavior. Proceed at your own risk. Your mileage may vary.