How do I convert the replays into a format that I can play with an ordinary player (So that I can upload the replays into Facebook). I've seen Toriash replays on Youtube so I was wondering if this was possible (or do they just use Fraps?).

It has to be recorded in a video format before you can put it on youtube.
When you save a replay its just, velocities, joint states and dismemberments all recorded with numerical values.

If you go into your Toribash folder, you can find your replays stored as .rpl files.
However, this is not an acceptable video format, so you have to use some sort of screen recorder.
Fraps is a widely known one, others are Hypercam and camstudio.

If you are planning to record replays, btw, shaders and /opt hud 0 will make it look much more professional.