Each module spits out compiled binaries to the "bin" directory, and these get checked in. So in theory you don't have to build any binaries except the ones you're currently modifying.
For the unit testing bug, it's a bug I see only when using the binary that's checked in to the repository. If I build the UnitTestSharp.dll locally, it works like it should. So first step for that one would be to verify that you can reproduce it. I was building Azimuth (the math library) when I first saw it, so just "rebuild" the Azimuth solution and check the output and see if it matches up with what's in that bug report.
For the parsing, see
clicky for an example for a float. It basically converts a string representation to an actual instance of an object. I just want something similar for Vectors. There's some methods set up in the code right now, but they just throw exceptions saying they aren't implemented for Vector. You need to write tests to verify that they work (check out the Scalar class's unit tests for an idea of what to test for and how to set up tests), and then actually make them work (ideally in that order, because it's considered good practice). It'll make more sense if you look at the code in Azimuth, I think.
I can break this down in to more step-by-step instructions, if you need. Part of the effort is just understanding Visual Studio and the basic layout of all the modules and how things fit together a bit. Browse the source a bit and see if it makes any sense or not.