Most premade tilesets include everything that needs to be done to make the tileset work, as that is a fairly extensive project on its own. To make a tileset work properly from scratch, you would have to make or acquire the art, then modify most of the creature and material raw files to tell each of them individually which tile to use, then do some init setting changes. The game client in the tilesetted folder will just refer to all of the modified files by default; if you wanted to use your "original" download, you'd have to copy the dwarf fortress/data and dwarf fortress/raw folders from the Mayday one to the original one, but that would just turn the original one into the Mayday one.
The Mayday version probably has no sound because of the init setting changes. Go into dwarf fortress/data/init and find the init.txt file. Open it, look for a line that says [SOUND:NO] and change it to [SOUND:YES]. It should be very close to the top.
The current version of Dwarf Therapist's forum thread is
here. To get it to run, you just load up your Dwarf Fortress game, then open the Dwarf Therapist client in a different window. It doesn't really "go into" the game, it just reads Dwarf Fortress's memory as it happens and alters it as you tell it to, so you'll have to either play Dwarf Fortress windowed or minimize it when you want to use Therapist.