You can install Synaptic. That is what I prefer. By default the package
manager is Kpackagekit which has been around for awhile, but I have never
grown used to it. There is also Muon which is supposed to become the default
package manager at some point. It is not part of the default setup now, so
you would have to add it to try it out. You can also install Software
Centre. I am not sure if it is installed by default because my system is a
hybrid anyway. Kubuntu uses Gdebi to manage deb files. This is what Ubuntu
used to use before SC took over that function with 10.10. Of course, you can
still use the commandline and use apt-get, aptitude (not installed by
default) and dpkg.

All of the package managers have built in search functions. I like Synaptic
for its ability to filter and look at status such as broken packages, the
repository origin and its listing of dependencies. Most package managers
don't provide enough information and SC is the worst offender. So although
slicker package managers come along, nothing does the job like Synaptic (for
me).

You do not need to download TBird. It is in the repos. You can even get the
Beta if you add the PPA to your sources. I don't know anything about your
Trash problem. Go to it with your file manager and see if anything is in it.
It is located at .local/share/Trash/. If you do not see the hidden folders
(beginning with periods), then press Alt+period in Dolphin or Konqueror or
Ctrl+H in Nautilus if you still have it installed (for GNOME readers). It is
not a good idea to use Nautilus in KDE or XFCE though because it replaces
the desktop with GNOME's desktop unless you add a --no-desktop option to
your launcher (just in case you are tempted).