Help! 1st time mom question..

Julii
Baby moves head side to side and swings arms and legs up and down .. Sometime when he swings his arms up and down he hits his face.. Is this normal ?? My son is 3 months old but he is a premie so he should really be 2 months... Is this just a stage since he is learning what his arms, feet, hands are?? What about moving face side to side..??