A.J.
It sounds pretty normal to me =) babies just get really excited at the world around them at this age! Babies learn by touch, taste, sound, etc. so that's how they explore their world.
You can definitely teach a baby this young! I started teaching my children as soon as they could scoot themselves around on the floor! When he grabs hair or pinches, tell him simply "no, be gentle" and gently remove his hand. When he bites, say "ouch! that hurts mama!" and tap his cheek very lightly to get him to stop clamping down. The key is that it takes 100% consistency to teach a baby. Repetition is how they learn. You may have to do it 30x in a row, but take it from me, he WILL learn and it will be so much nicer for everyone involved once your hard work pays off!
Interaction with other kids is a great way to have new situations pop up where you can teach a lesson. I would start out with playdates with moms you know who will be more understanding to the situation. Once he learns to be more gentle, then you can take him to classes like Gymboree, library story time, etc.
Also, you could get a baby doll to help teach him to be gentle. Teach him to kiss and hug the baby. Teach him to pat skin and hair gently. This is a great opportunity to introduce new language ("gentle", "soft", "kiss", etc.)
Also, when babies bite, it's usually a sign that they're teething. Try giving him some orajel to ease the pain and teething rings, teething biscuits, even just a wet washcloth to chew on.