I had a Simon security console in my last home. It was X10 compatible IF a X10 interface was installed. At the time of installation, the tech made it sound like everything was proprietary and had to be purchased through him, but he didn't have the module and the price was steep anyway. I believe that if you can get a compatible adapter, you can use your console in some limited ways to control X10, but it's not going to be a full X10 system. I think the system can flash lights, turn on sirens, etc.
In my opinion, if you want to control things over the internet, the Simon is not necessarily something that would be involved in the discussion. What you need is a controller that can connect to the internet and interface with the mains to send (and possibly receive PLC). Currently, the MyHomeOnline plugin for AHP will not work since the X10 server is not available. As Brian H stated, the new owners of X10 have a WiFi module that is in development that is likely exactly what you need. I do not know what kind of software will be included with that to make it work on the internet (WiFi is local to your residence obviously).
Alternately, you could opt for a software that will interface with a X10 to PC controller that has internet connectivity. I don't know all the options as I've never connected over the internet (only my local network). I know that the software I'm currently using (HomeGenie) has the capability listed, but so do many others. Someone else might be able to provide a better suggestion if you want to go that route.