I've generally kept DB3 targeted against the latest .NET SDK. The last one wasn't very impressive, but Soon there's going to be
fun stuff to play with, so I'm trying to keep it targeted against the latest SDKs and IDEs.
You may be able to get the program to run against Mono. 99% of the code is just generic C#. The math library Azimuth has a C++ preprocessor that was compiled for Windows, so that wouldn't run on linux, but it might run on XP. The graphics library is targetting DX9, so that too won't work on linux (without maybe Wine or something along those lines) but it might work on XP. But I'll definitely say XP is not a supported platform (in fact, the only supported platform is whichever one I happen to be programming on

Right now it's windows 7, but I might go to win10 when that's a thing).
If you're sticking with XP right now because of cost, I hear rumblings on the blogosphere that Microsoft is thinking about releasing a version of windows 8 for free.