Although this is typically not what you want (imagine any site being able to execute files on your local machine), this is not so much a Mendix question as a general web app question. You could check out this thread from StackOverflow. Note that certain restrictions may apply: e.g. you may need to add a key in your registry, it may only work in IE, or you may need to download an extension for Chrome (if you choose the go the ActiveX route).
Keeping applications in sync would typically be done by API's, or by (manually) importing files. It depends on what NX supports: I am not familiar with the application.
I have a similar use case. I'm wondering whether the NX Open for Java remoting capability may come in useful. I'm hoping a remote NX server could be run, and accessed from a Mendix driven client. There is some info in the docs and some examples in the NX install directory.
Hoping to give this a try in the next few weeks - if anyone's tried this or has any other suggestions I'd be very interested to discuss!