Re: Alarm doesn't work when phone is off?
I think you've either misunderstood what the OP wants or what these apps do. PowerBoot lets you schedule a reboot - phone is on, pre-set time arrives, phone reboots. That would be fine for someone who just wants to reboot regularly - it won't be a clean shutdown, but if it's in the middle of the night and the phone isn't updating anything you'll probably be ok.
What you can't do is set the app to reboot at say 06:50, turn the phone off, and expect the phone to turn on at that time. It won't work for exactly the same reason the alarm can't do this - the phone is powered down, the app is not running, so it can't boot the phone. You need to build that sort of thing in at a much lower level (ie hardware that will remain active while the rest of the board is powered down), and can't just add it in with an app.
This isn't theory - I installed the app just now and tested it. The phone did not switch itself back on.