Is it normal for my baby to be teething on his hands?

Yes. Sure, hands and fingers are like built-in teethers! Plus, they're hard to leave at home or in the car!
Yes. Absolutely! Most babies find comfort in gnawing on something, and of course the most convenient item is his or her own hands! Certainly a teething toy may be helpful to many infants. Interestingly, neither of my kids took to a teething toy, but preferred their own hands (or my knuckles!) they will outgrow this phase after the teeth come in, so not to worry. Bibs are also helpful for all the drool!
Yes. When a baby is teething anything is fair game. The hands are the most convenient way to teeth.