She's behaving this way because it gets a reaction -- from you -- apparently her likely target. How does husband discipline daughter? I'd bet that he's been firm with her and she because of time spent with him also knows his limits well.
With you, its a toss-up as you and her probably haven't spent long hours together too much due to your work schedule. She's a smart one -- she's going to gamble to get to your path of least resistance, which seems to be screaming and full body fits.
You say you don't know what to do --that's exactly the reaction she wants -- complete frustration and inaction on your part, or inconsistency as you desperately seek to find her off button.
Unfortunately she holds the off button herself and all you can do is return her the favor of manipulation by completing ignoring her fits and I mean by acting completely as though you are deaf and she's also invisible. No reaction. No change of policy.
She'll ramp up the volume but only so far, we've all got a point at which we give up. Just remember that the longer she's been used to getting what she wants with that behavior the longer its going to take to break her of it.
As for the screaming when excited, just simply modeling other behaviors to express excitement and possibly just a gentle (non punitive or frustrated reminder) that screaming is not necessary. Again, you don't want her to associate screaming with an action that gets an extreme reaction from you.
As for the biting, such behavior should get immediate reprimand and punishment, as well as scorn from everyone. At that age, children need reinforcement and will seek where ever they can get it, use this to advantage -- ostracize bad behavior (never scorn the child -- the behavior). Again, she is doing this as it gets a reaction and she also is only two years old -- with proper guidance she'll break the behavior before it becomes a bigger problem.
My daughter was sent home once for biting a child, then a daycare worker all in a matter of an hour. She was six. She was punished, she never did it again. The teachers also got my permission to isolate her if she was overly aggressive or physical with other children from that time on. Again, it worked, she learned to temper her impulsiveness.
Forgive me if I sound pat, but I raised three children, my middle one was a holy terror on wheels the minute she came out of the womb. I know those screaming tantrums and excited screams well. My ex-husband encouraged the behavior so once I divorced I had a hellion and a half on my hands. But, ignoring the bad behavior, positive reinforcement for good behavior (playing calm, not fighting with others, being gentle) got rewarded.
Even after nearly twenty years, one still doesn't forget :)