Will Firefox work on Windows 7

Yes, Firefox 3.0, 3.5, and 3.6 will work on Windows 7 just the same as they did on previous versions of Windows. When the Firefox window is open and visible in the bottom taskbar, there will not be any added options like some other Windows 7 applications.
For instructions on how to install Firefox, see Installing Firefox on Windows.

64-bit?

Firefox will work on the 64-bit versions, but it is not a 64-bit application.