Is it normal for my baby to twitch in his sleep?

Yes. Babies will twitch while in the rem (rapid eye movement) phase of sleep. Babies may also flutter their eyes beneath their eyelids or seem to startle during sleep. Twitching of the face or jerking of the arms and legs during sleep is something the baby will grow out of.
Yes. I would add to dr. Hall's answer that infants, unlike older children and adults, enter during rem sleep and it accounts for approximately 50% of sleep time at birth. It is also characterized by irregular breathing and occasional vocalization, all of which is normal.