Run and build Visual Studio project on Mac OS X
Although you will get more info from Windows/Mac developers on StackOverflow, I can tell you that depending upon the project and its dependencies, you might get away with it or you may not. Of course nothing Windows related can be run on OSX, so if you're only doing a "hello world", chances are you will be able to run it, provided you have the right toolchain to build that (gcc++, etc.)

Regarding whether there's a "Visual Studio Compatible IDE" the answer is "no" (unless you consider MonoDevelop which works 'ok' for some things).

The solution, of course, is to use one of the virtualization alternatives (Parallels, VMWare) or simply have a windows partition via Bootcamp.