You will 100% DEFINITELY NOT require the disc to be in drive to play the game once it is installed.
GUARANTEED.
Also, your product key will also be saved onto Steam so you can lose the disc/product key and still be able to play the game and reinstall it as many times as you wish.
Regarding updates/patches, updates will be downloaded/installed automatically without you having to do anything
There has NEVER been a Steamworks title which requires you to install updates "manually".