My Pullet Shut opens into a (hopefully) secure run, so haven't had anything in there trying to open it. But, I don't imagine they'd be able to even if it were exposed. The motor keeps it shut, and it fits tightly into the frame where the edge can't be accessed easily. If the door shuts too late, put the sensor under the eaves, under the house, or behind a post where the sun/floodlights don't hit it directly. Should close earlier that way. I've got mine under the eaves, and the door is closing at dusk (9:00pm).
As far as perching on the door, that hasn't bn a problem with mine. It's too narrow for the girls to manage that; It would be like them trying to perch on a piano wire.