When actors are acting in films, can they see the camera, like in their peripheral vision?

No, they go camera blind...

They also don't hear the director shouting "Action" and "cut" either.

They do. They used to act with it in mind. But then that dude from Gone with the wind stopped doing that. And the rest have adopted his approach.

They might look to get cues from the director, is all I know

Yes, of course. It is directly in their line of sight.

Of course. Doesn't it seem "suspicious" that actors NEVER look directly into the camera? They can look literally everywhere else but the camera so they sure as hell know where it is.

very much. the cam and lihgts are the biggest things in the room.
kike having a car in your living room

Absolutely. Those things are huge.