same same here, my boy is 2 months and he also keep rubbing and scratching his face. he even scratched his eye and caused an eye tear that requires us to take him to doctor but doctor say it will heal on its own. my mother in law let baby wear mittens so he won't scratch his face. and to answer your qns, my PD said it's normal for babies to learn to fall asleep as not all babies are the same. they will outgrow this phase.
My baby used to be able to soothe herself to sleep when she’s around that age. Now she’s 6 months old and we need to pat her haha
Tania