We fostered a 5yo and 2yo- it DEFINITELY gets better! I still vividly remember the first MAJOR tantrum our 5yo threw! I definitely thought I was in over my head. The best advice we got is to completely ignore the behaviors you don't like. This is really hard, but it REALLY works. And often times we would praise the 2yo or even DH for display good behavior. "Oh DH, I just love how you sit at the dinner table so calmly so that we can eat dinner together and talk about our day. It is just so nice to be able to have a great conversation with you!" or "Oh 2yo, you are doing such a nice job playing with your toys gently. It is so much fun to play with our toys gently so they won't break and we can have fun with them again tomorrow!" while you ignore, ignore, ignore the bad behavior. And the bad behavior will escalate before it gets better. But this technique worked wonders for us.
Hang in there! And enjoy the new-ness of it all. I was just thinking back to those days as we were discovering their personalities.