Q1: Steam is a separate program & it stays resident in the taskbar.
You need to manually exit it from there (right click -> Exit), I do this but people who play lots of Steam games might leave it open.
Currently minimised to Taskbar its using 7-8MB of RAM, eg compare with Adobe Reader 9 with no pdf open & the ATI Catalyst Control Centre (ccc.exe) minimised to taskbar using nearly the same amount.
After the resident icon is closed down, Steam.exe disappears completely from taskmanager.

Q3: Steam games all install within the Steam folder on your PC (you can choose the location of this folder).
Other than shortcuts, I'm not aware of any files stored outside the Steam folder.
eg you can simply copy the Steam folder to a new PC, make a shortcut to & run steam.exe, enter your Steam username/pwd & your games will all be there.
Alternatively, if you have lost all your Steam content, you can download & install the Steam client (a few hundred KB) & as long as you remember your username & pwd, it'll download all the Steam content associated to your account.