I can't really visualize your setup fully by your description, but it sounds like your 4-way fitting is a sanitary cross on it's side which leads towards a drainage stack, which would explain why you are having toilet water push into the lav/shower drain. And the piping should have been sloped 1/4" per foot, not 1/8" per foot. Your shower drain is wet vented, but you shouldn't be experiencing problems from the lav sink draining if the piping was done correctly. Who knows what this "plumber" did, but it's obvious from the problems that you describe that he didn't do things very well or understand wet venting. I seriously doubt this guy was a real plumber.
Your only bet at this point is to open the ceiling from below and see what this person did, have a real plumber come out and verify the piping, and then threaten the original guy with a lawsuit if he doesn't hire a professional to redo it properly.