You need to call Alarm Relay to make certain they can work with your ADT system. Hopefully, they don't have some proprietary reporting system coded into it. Which, frankly, wouldn't surprise me. So cross your fingers.
You get 24/7 monitoring. The service central stations provide is pretty much the same across the board. They will contact the Police or Fire department as needed as well as yourself, friends or relatives based on what you tell them to do. For example, we have many, many power outages and I have instructed them not to call me when they occur.
Yes, they can cut your phone line. I am using mine with VOIP provided by Comcast and they can cut that line too. A cellular backup is the only sure way to ensure protection short of a catastrophic breakdown of our infrastructure.