This may be a dumb question, but does a job stop running on a Colab instance when I close my browser? If not, is there a way to keep it running (i.e until it's complete)
In that same vein of thought, if I were to give someone edit access to my Colab notebook, would it be running on my instance of Colab with all my installed libraries or on theirs?
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.)