Is my 3 year old normal?

My 3 year old son is driving me and my husband crazy! He is a very active child who has been getting help with his speech delay for a year. As a baby he was happy and content but did not go through typical baby milestones. For example he never went through the play phases of putting objects in or out of things. Singing and acting out songs like "its'y bitsy spider. He never used the word no until he was almost 3. He is social and has been ruled out for any kind of autism. Having said that i still feel like something is not right with him. He was this calm content baby untill he reached 18 months and than he became this super active, emotional moody kid. He does not seem to respond to time outs, verbally it is really hard to explain things to him and he often makes the same mistakes over and over again. For example if we are at the park and he wants to play with something that could be harmfull I just end up having to take him home. Because he will not respond to "you could get hurt if you do that" In my mom's group all of his peers seem to respond when their moms give simple explanations for why not to do something. I have to ask him not to do things over and over again. He does not respond to my voice for example if he is about to do something that could cause him or his baby brother harm and I raise my voice or talk with urgency he is unable to pick up on that and will often continue doing what ever it was. We have tried distraction and that does not work as often as we like.
I wonder about auditory processing problem?
He is so moody and he screams at the top of his lungs when he is upset which is very upsetting to my husband and I. He is very unpredictable about what upsets him. But lately it feels like everything is a struggle. It is starting to affect our whole household and I am starting to feel resentfull.
Is this normal? I worry that I am doing something wrong with my parenting. I always prided myself on being good with kids until I had my own.

[Encephalomalcia]

Sounds like a normal 3 year old to me.  He may be more active, some children just are.  It is good that he gets his moods out instead of bottling them up inside (those are the kids I worry about, the extreme quiet ones).  If a child feels safe in his environment, then he will be comfortable enough to act out when upset.  Also, if he is picking up on you and your husband being irritated, he will act out more.  You need to be calm and happy.  

[katlynruth]

I know this is old and I am not sure if you are still on here but this can be a problem with hearing. Number one sign is that he doesnt respond to your voice. Even infants that do not comprehend words can read the tone in a persons voice. I test hearing and a moody child that was slow to speak is the first sign I look for.