To shut down immediately after clicking Shut Down or pressing the pc button there's the command Adithyansm provided which I agree with, gsettings set org.gnome.SessionManager logout-prompt false, was already asked on Eliminate shutdown confirmation and approved as a solution. Mind that the 60 seconds delay is a safety measure to avoid accidental shutdown or give you a chance to abort shutdown if you suddenly remember you forgot to do something so unless you aren't sure you really want to shut down your pc when you click or press the button to do it you can proceed with the command.
Looks like buttons are enabled before the touchpad or buttons are detected when pressed instead of touching the touchpad, not sure about this difference, can be a hardware issue.
As Adithyansm I think there's no way to login automatically when password is correct, for security, because let's say that your password is 12345 and someone knows you, that you like things so simple or maybe even saw you type that password for a while (not the whole password), that person starts typing numbers and even without trying each time to hit Enter (I mean after each new number combo, one after the other, like 123, then 1234, then 12345) that person will access your pc with few efforts.