In a library file (dll) I know you can modify an existing property and the exe continues running without recompiling.
If you add properties to the dll class and if it isn't critical that the exe knows about them, would the exe continue working without recompiling? Personally, I'll bet not, but I'd like an answer from someone who knows.

Depends. If you use versioning on the DLL then yes it will notice and you will have to recompile. Otherwise, no, as long as nothing it needs changed, it should run fine.