Hi Yashiro,
You might need to look into the PushRegistry API.
However, what you describe will not be possible. It is not possible to let a process be started and executed automatically. In other words: the user will always be prompted if he/she wants to launch the autostart registered app, every week. I could not get this prompt away, with or without having the app signed. However, this last thing might differ on certain devices; I can't confirm that.
And, it is only possible to set one autostart time (when I am right it was a long value referring to the amount of milliseconds from the current time on). So, it is not possible to specify some schedule like "every week". You will need to re-register a new (i.e. next alarm time) PushRegistry autostart entry everytime when your app was launched.
And, the user needs to start the application manually on the very first time (so, after having installed it on the phone). It is not possible to install the MIDlet and register an PushRegistry autostart entry automatically.
Good luck!
Jasper