On the fastdl server, everything in the /gamemodes/terrortown/content/ directory may need to be copied into the main /garrysmod/ directory for the downloading of TTT's textures and models to work correctly.

However, all your players will already have the textures and models and stuff through the gmod update, so they won't actually download anything other than the Lua cache file. As such, the copying is probably not necessary.

Nothing changes for maps, and nothing changes for custom textures or models.

The TTT Lua stuff was always in gamemodes/terrortown. The textures and stuff used to be in /materials/ etc, but is now (in v9) in /gamemodes/terrortown/content/materials and so forth. If that's what you mean.

The update didn't do much to the gamemode itself, but gmod servers have been breaking a lot in different ways. They've released a number of patches since the big update, so make sure you try to update the server's gmod version regularly. I just ran the update tool on my testserver and it updated gmod to version 86.

Can you see if there are any errors in the server console?
Are you using sv_downloadurl/fastdl? If yes, have you tried turning it off to see if that helps for the cl_init error?