Rubbing eyes can be a sign of tiredness. It’s very normal behaviour:) you don’t need to prevent it. Just respond to it by letting baby rest. Clenched fists are also normal in newborns. The hands open up a lot more after 3 months. Nothing you need to do too:)
https://parenting.firstcry.com/articles/baby-rubbing-eyes-reasons-and-prevention/
Clamped fist not meant scared. Baby always clamped fist in mitten.