Can I access USB or Firewire drives connected to my Mac?

Yes.

Note, though, that if nobody is logged in on your Mac, external drives aren't available. If you log out for security reasons you might like to start locking your screen instead, or use OS X's Fast User Switching.

Alternatively, you can make your external drives available even when logged out by running the following command in Terminal:

sudo defaults write /Library/Preferences/SystemConfiguration/autodiskmount AutomountDisksWithoutUserLogin -bool true

Can I access shared files on other computers, or the files on my Time Capsule?

Yes, but only if your Mac is already connected to the share (although see below). Your options are:

But...

A future release of FarFinder will handle the process of connecting to (ie. mounting) a new share. This is available to licensed users now, in a preview release - see the downloads page.