I'm not sure if this is normal, but whenever I join a GMTourney (for example) I have to manually get the mod from the Mods tab on the forums and then restart Toribash just to get the mod working. Does anybody else experience this issue or is there just something wrong with my Toribash?

Mods are auto-downloaded, you have to wait until next fight for them to display.
Or do you have some major issue with textures not loading as well?

I have the same issue with textures, flames, and 3D items. I have tried reinstalling already and it still doesn't work for me

if it's about mods, type /rec when you get in the server.
As of player items, type /dl Playername for the items to download.
All I can do, if that doesn't work there might be something wrong with your PC