as for #1, the app is supposed to get "woken up" and put to the foreground by a "push notification" sent to the phone by the mitel server. Sometimes it can take a while to get through but if it doesn't work at all then something is not working correctly.
Once the app gets in the foreground, it connects and re-registers with sip to MBG and then MBG will forward the pending INVITE to the set via that sip connection and the ringing should begin.