We have the 2008 version of your trailer.
The front compartment leaks are tough, at least in my experience, to completly cure. If you are ever able to see the amount of water that is hitting that area when you tow in the rain, it probably wouldn't be a surprise that some of it finds it's way in.
Things to look for or check and possibly fix yourself are -
The gasket around the door - is it crimped, twisted or pulled way from the coach?
Do the latches feel tight when you twist them to lock?
If you note problems in either of those areas, you can probably adjust or repair it yourself. A bigger issue is to check the corners of the door frame, especially at the bottom. This is a relatively high stress area and others have reported cracks in the skin in this area which leads to leaks.
The styrofoam in the bathroom is a little puzzling. The only source that I can think of readily is the insulation around the water heater which is under the sink. Maybe you need to open that door and see what's gooing on. There could be something rubbing the insulation and causing it to break up.
As noted above, North Dallas RV is probably your best and closest place for parts. Roger Williams A/S in weatherford is also highly recommended but they are a bit further away. Explore RV in the Mesquite area has Airstreams on the lot and provides some service. I haven't heard anything about their service and I don't think they have a parts department there though
I believe the sensors for the tanks are actually outside of the tanks and work based on pressure. I doubt there is any gunk on it, but it could be out of calibration. There is a calibration process, but it is kind of a pain to perform. It could also be a bad sensor which would likely be a dealer repair.
Sorry - can't help with the flush system. Mine seems to work as advertised, but it sounds like you may have a leak of some kind on the route from the connection to your tank.