The favicon and metadata are both set by the theme.  In Totara 1.1 and 1.0 this will be typically be edited in the theme's header.html file.

In Totara 2 this is a little more complicated; if you are lucky then there will be a layout directory in your theme and you would need to edit each of the php files  in that directory.  Your current theme may be inheriting this layout file from a different theme though, in which case I'm sure somebody else here can give you a hand (I'm not a theme expert)

Note that browsers can take a long time before they start picking up the new favicon.ico file, so try it on a totally new machine if you want to test that it has been uploaded succesfully.