Any touch screen phone will activate on the edges. A case with a raised edge might help you avoid that.

Enabling Settings—Display and Brightness->Raise To Wake might help your Face ID issue, but also make sure your IOS is up to date.

Sunglasses can interfere with Face ID. You do have to LOOK at the phone, which sounds funny, but I’ve seen people not looking and expecting it to open. Then they get annoyed and look at it :)

Another way to wake up Face ID is to swipe up from the very bottom of the screen the instant you pick the phone up.

If it still acts up, redo your Face ID. Maybe you got a barely working scan the first time.

And yes, this is the kind of thing your phone should suggest if it notices that it’s slow when you pick up.