I was trying to update Firefox, and I have just downloaded the .txz package of Firefox (52.2.1) and covered up the older version (45.2.0) with the 'upgradepkg' command.

Firefox can be executed fine. However, the interface does not seem to integrate with the KDE-default 'oxygen theme'. I wonder how I could bring back the old looks that match the system better.

In addition, I would like to know a better way to update programs, since my Firefox never showed that 45.2.0 needed updating.

to update Firefox to latest maybe try ruario's script? HERE

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A couple of points, limpingstone
The Firefox in Slackware has its "Check for new version of Firefox" routine disabled. This prevents un-vetted changes from coming into Slackware blindly. For example assume the "New Official" Firefox depends on a version of, oh say, gconf or glibc even. If updated, it might be "broken" by lack of some dependency or other.
The "Slackware Way" to update your system is to simply run:
Firefox will receive updates as they are pushed out by Patrick. So the version may lag a bit. This is normal.
If this is undesirable for you, Slackware makes it simple to bypass this, and take matters into your own hands. Simply uninstall Firefox, then download the official ?.tar.bzip? from Mozilla. I recommend extracting that to an out-of-the-way place like /home/user/.local/firefox.
Then create a softlink from the binary:/home/user/.local/firefox/firefox to a file you create under /usr/bin, and call it firefox. From then on, you can launch firefox normally, and it will seek updates on its own (I think by default). If you go this route make sure to blacklist "mozilla-firefox" in /etc/slackpkg/blacklist

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