A couple of things:
1) Attachment issues can be present even when a child can go to bed and school without problems. So even though he goes to bed fine he might have attachment issues from going back and forth between different caregivers in his young life. And you don't know what he experienced while he was in his biological mother's care.
2) I know the community mental health centers around me (don't know about other parts of the country) have what are called infant mental health programs. They are programs to help children ages 0-6 and their families. There doesn't have to be a problem to participate, it can just be as assistance/prevention. For all that young babies sleep and eat, cry and play and poop, a lot of development is happening at that time.
3) You are right about the need for consistency. However, I would suggest against hitting, pinching, biting him back because he does. This teaches him that it is okay to do to someone what they do to you. And I assume that isn't what you want to be teaching him. Instead let him know verbally that he is hurting you (even if it doesn't actually hurt) and then give him a time out.
4) When he becomes upset/emotional try to verbalize for him what he might be feeling. Since he is still young he will be having trouble verbalizing his feelings. Help him calm down so that he can talk about his feelings with you. He needs you to help him be able to regulate at his age. So if you can figure out the cues he gives off to tell you he is starting to become emotional you can step in and help him regulate before he becomes violent. It can be hard to figure out what those are. Start with triggers. Sometimes it can help to see if he becomes upset in similar situations, times of day, etc. HALT: hungry, angry, lonely, tired is a good starting point and move out from there.

Good luck.