It is normal. Now it will last for weeks or months if you choose to ignore it or do the reward chart when he doesn't misbehave....or you can do like every mother in my family for at least three generations punish him if he hits or hurts someone.
It's very hard when they are in daycare, so I'm not sure how you will handle that one. Maybe you can tell them to put him in time-out each time he hurts someone. (And not the silly two minute time-outs...my rule: they sit until they cry..because if they don't cry, they don't care)
I would also reinforce the punishment at home if you get a bad report. Worked for my mom. She always said you get twice at home what you got at school. We understood this at a very young age.
If you sit down and talk to him about hitting (then act out hitting so he knows what you are saying) and so forth and tell him it is wrong to hit your friends. (act out the biting thing too) Then tell him he will be punished if he does these things. It is best if you can catch him in the act.
Would the daycare allow you to spend a day watching him (without his knowledge) so that you can catch him and then punish him in a bathroom yourself. That way he will know that mommy is serious.
The daycare situation makes it hard, but you will need to find some way to get through to him because it isn't fair to the other kids that have to endure his acting out.
And as far as the bed goes...the way you handled it with letting him cry for a bit and then soothing him a minute was good. Just don't give in. You make a rule...come Hell or Highwater...you stick to that rule.
He's beginning to get a sense of his own will and he is going to test all his environments. You have to put your foot down as a parent and insist that he behave. No ifs ands or buts about it.
He's normal so don't fret. You didn't do anything wrong. It is easy for a child to be bad....we have to teach them to be good. (for most kids anyway)