Another app is currently holding the yum lock; waiting for it to exit

That is PackageKit attempting to update the yum database so that it can show you a desktop icon when there are updates to apply.

It should only run for short periods - if it is failing to complete then it suggests there is some sort of problem with your yum configuration such that it is hanging trying to update the status of one of the repositories or something.

If you really don't like PackageKit, you can remove it by running the following command as root:

 yum remove PackageKit

You can also disable PackageKit from checking for updates by running gpk-prefs from the terminal:

 gpk-prefs &disown

In the preferences window, change Check for updates to never.

Stop the daemon of packagekit with:

service packagekitd stop

I don't remember if the name is "packagekitd". I also don't remember if in the last versions of fedora PK is a daemon or only a user process.

If you want disable the process check the command "ntsysv" as root in a terminal and the autostart applications in your desktop preferences.

For your problem with the internet connection and the download of packages, check the plugin fastestmirror for yum. The configuration is very simple. Also use the presto plugin.