Does Google Colab stay connected when I close my browser?
The current cell will continue executing once you close your browser, but the outputs will not end up in the notebook in Drive. (If you were to reconnect before your VM were considered idle and deleted, any values you'd computed would still be available in your kernel.)
Distinct users are always assigned to distinct backends, so they'd have to install the libraries themselves. (This is one reason we encourage keeping library setup/config in the notebook.)