Does the application JavaFoil run on x64 machines?
Yes, the application is running on x64 machines, but you will have to add the official website to the Exception list in Java Control Panel, because the app is deployed as a JNLP which means you will run it from the website.
Use the following website to access the installation instructions where you can see download links as well: http://www.mh-aerotools.de/airfoils/javafoil.htm