Every child is different and responds to different tactics. When my son used to throw tantrums (2-3yo) I would stand and watch and actually encourage him to do "better", basically telling him "If you're going to do something, do it right." After a few tantrums he realized that he was not getting the reaction he wanted and quickly decided not to throw them any more.
Our youngest daughter didn't respond to any kind of spankings or time outs, so we instituted the "bad girl chair". Sort of like a time out, but in full view of the entire family. She had to sit in the bad girl chair while everyone else went about their business. She quickly decided she hated being "viewed" and so obviously punished while everyone else was having fun.
As for the biting - I bite back. For some reason children bite, and they don't seem to realize that it hurts - until someone bites *them* (not too hard, mind you, just enough for them to realize it is not a nice thing to do).
Keep trying different approaches until you find something that works. For some it's physical discipline, others it's mental...I know it's difficult but eventually you'll find the "way" to deal with the situation that achieves the desired results for the child in question. My oldest 3 are now all teenagers/college students and honestly, they all required different tactics throughout their lives. Exhausting, but worth it.