Take a look in /var/log/rpmpkgs to see which version of yum is installed, also go to updates site via the link at the top of firefox to see if there is a newer version. Download the latest one at the Fedora update site for your architecture even if it is the same one that is installed, or if you have kept all updates in /var/cache/yum/updates/packages, then you will have it already. Remove the one installed with rpm erase command using the full name of the package which would probably be listed in /var/log/rpmpkgs with similar command:
rpm -e packagename.rpm
Then install the latest one via command line from the directory it is in with similar command:
rpm -ivh packagename.rpm
If the package at the update site is newer than the one installed, you can probably just update the installed one without erasing and reinstalling with similar command from the directory it is in:
rpm -Uvh packagename.rpm
As for finding out what all it's dependencies are you would have to read 'man rpm' to find how to query a package's dependencies, I know it can be done, but I've never had to do it.