It's not dead, it's just resting.

The one with the bird looks like Peregrine Falcon nesting boxes I've seen on skyscrapers around here; I suspect the bird's sleeping.

Bird's feathers are moving slightly, seems to be alive to me, unless there's a fierce wind or something.

just moved his head

Yep. Bird started voluntarily moving. I was getting concerned.

Concerned for the bird, or concerned that someone had a webcam stream of a dead bird? :)