biting - the best advice I was given for a teething bite is to push the face into the breast so the baby can't breath properly and unlatches - that's a quick and easy way to get them to unlatch fast. Do NOT under any circumstances pull away as it makes the bite worse. Then wait a few minutes and resume the feed (if you can bear it!)
However as they get older I think it's usually more about getting a reaction and they need to understand there are consequences. I tell DS1 that he has hurt me, if I think it was an accidental nip then I resume the feed, but if I think it was deliberate or if there is a second offence then the feed ends - no third chances. He has quickly come to understand that any messing means losing the feed so he doesn't do it often!
Tantrums - DS1 is not a very tantrummy child fortunately but I am a great believer in just ignoring whenever possible. At home I will usually shut the door, say loudly "come and see me when you are ready to calm down" and go into another room. When he has calmed down there are no recriminations, just a cuddle. Out and about is more difficult and I usually end up wrestling him into his pushchair (fortunately he can't manage the clips yet) and driving off at speed...
But there are lots of other good threads about this if you search the archives.