M.K.
The very first thing to do is address the dangerous behavior (hitting, biting, anything that causes physical pain), and do so immediately.
I'm a huge advocate of time-outs. However, you'll need to "up the ante" when it comes to the hitting. Consider a time-out in a solitary area (where he cannot see you or hear you -- such as a playpen in another room or in his crib). Make it clear to him that there are no warnings and no second-chances for hitting. As soon as you see the hit, you immediately, calmly, remove him and put him in his solitary timeout. If he throws a fit, you let him calm himself down and then go get him. He will very quickly learn your NO TOLERANCE rule for physical violence. Get this taken care of before your youngest learns it herself.
As for the other behaviors...well, just wait for a few more months until your youngest starts fighting back! :) I wish I knew an easy way to get young ones to be kind to each other all the time. Positive reinforcement, modeling kind behavior, etc. is all I know, and you are already doing this. Once he turns 3, you'll be able to leverage privileges (take away an outing, give extra books at bedtime, etc.) to help influence his behavior, in addition to time-outs.
You can't change everything at once. Hence, I would put 100% of your efforts into the big problem, and tackle these minor ones once you have things under control. Good luck!!