Standard JavaME doesn't offer any way of making background MIDlets.
But some phones lets you do Display.setCurrent(null);
in order to hide the GUI and show the phone UI instead. I've seen it work on Sony Ericsson phones, but I'm not sure if it works on Nokia devices. (I don't think so).
With the Asha models, Nokia introduced a whole set of new API's though, so maybe you can do it using one of those. I haven't been able to find any such option myself though.
As for the permission prompts, there's sadly only one way to get rid of those, and that is to sign your MIDlet with an expensive certificate, for $299 - each year...
A few phones lets you manually set the security settings though. I've seen this too on a few Sony Ericsson phones, where you can set stuff like "Only ask once" or "Never ask" for certain operations like "Camera access" and such. Don't think Nokia offers such options though.
Finally, it's possible to patch / hack the phone to kill the JavaME security. But again, I've only seen it on Sony Ericsson phones, and I don't know of any way to do it with a Nokia phone.
So I'm afraid you need to look into signing.