http://qik.com/ does at least the first two. Not sure about the 3rd.
That's the thing... you want it to. If you're pulled over by the police you want to 1) start recording, 2) start uploading to a server in some other jurisdiction 3) Lock your phone so that police can't see that it's recording/uploading, 4) the power-off button is disabled.
A police officer noticing your phone during an arrest and clicking on "stop recording" is a totally different situation than him asking you for your password.