Lirc I don't know about. Mplayer I know much more about.
DVD's sometimes use encryption to protect the data from being copied. Completely worthless trash, but there are legal complications that distros like Debian and Fedora want to aviod so that they don't install things directly.
In order to play these files you need to have a special software library installed called libdvdcss. It should of been installed along with the Mythtv stuff, though. To play dvds in mplayer what I do is go from the command line:
mplayer dvd://
If it's not able to find your dvd player for whatever reason, you would go:
mplayer dvd:// -dvd-device /dev/hd#
were hd# == your dvd device.
Then on top of that there are a few more command line switches for things like subtitles or if they offer different sound tracks (like you may have a spanish version, or a english version or a english + director comments version). It can get pretty silly with all the switches and stuff. I generally only worry about that stuff when using mencoder to rip dvds into AVI files.
What makes a MUCH easier and mostly better DVD player is Xine media player, or VLC media player. Of course you can use Mythtv's frontend to play DVD's, but I never done that before.
For installing other things you can use Apt-get. Now I am not so sure about the details on Knoppix when it comes to how they got it setup, but Knoppix is Debian-based and is compatable with debian packages.
So you should be able to do this:
apt-get update
apt-get install xine
Or something like that. (if you don't already have Xine installed)
Like I said, I am shaky on the knoppix details.
If it is just a problem with mplayer or whatever not finding the DVD player you can make it easy with a couple symbolic links.
You have your /dev directory, right? Now in that directories you have all these files that represent hardware and system resources. Like /dev/hda will probably represent your harddrive.
So what you do, if it isn't already done, is create a symbolic link from your dvd drive to /dev/dvd. That way programs can find it easier. You can do the same thing for your cdrom. If it's not done already.
Symbolic links are sort of like shortcuts, but a bit lower level in the system. They are basicly a way to create 2 names for any one file in a way that programs can transparently use them.
So say your your /dev/hdc is your DVD IDE device. You would go like this:
ln -s /dev/hdc /dev/dvd
edit:
Not sure on the wifi card though. it uses Madwifi drivers, I beleive but beyond that I am not sure. The drivers for the redhat and others probably won't work, unless you compile from source code for them. Best to ask a the knoppix.net forums for what to do.