If you want your LabVIEW program from Windows to run on Linux, you need to compile it first with a LabVIEW for Linux version. Be aware that path management is slightly different under Linux. So your Windows application won't run under Linux if you don't prepare for it.
If you want a LabVIEW / Windows application to interface with LabVIEW / Linux, you can do this with TCP/IP functions, or perhaps even with global variables (not sure if they work under Linux).
Can't help you with the second question(s). I'd be worried about getting any camera working under Linux and LabVIEW, but I'm not sure if this is a valid concern.
Regards,
Wiebe.