If each transmitter picks up the rebroadcasts if its own signals, then with some assumptions about the rebroadcast lag (or measurements of it added to the signal!), that's enough to know the range to each other transmitter, right? So maybe they do that and then just broadcast the ranges (tagged on to their main signal), then any remote receiver can work it all out from there.
Only in a flat environment without too much atmospheric distortions. As soon as you get multipath effects from eg waves bouncing off buildings and mountains then the computational complexity goes through the roof. Also I don't think you should underestimate how much the signal degrades in a "target path" vs the "direct path". The article mentions -60 dB and I think that is fairly optimistic. The transmitter power needs to be HUGE to make it work, so it would be much easier to have stationary transmitters. Normal radars manage to do this because they are highly directional, but multistatic radars need to look in all directions at once and need to up the power as a result.