Yes if you upgrade your application to a newer version of LabVIEW. If you don't, there is a chance it could still work, but LabVIEW 7.1 came out years before Win7, so obviously it's not guaranteed to support it.
Unknown. Version 7.1 is not supported but some people have installed it. There could be all sorts of issues with hardware drivers that the app is using. You need to provide a detailed list of the hardware and the drivers being used. Best thing to do would be to upgrade to a current version of LabVIEW and rebuild it. Even then, there could be problems that would require a major rewrite. For example, if the old app used the obsolete DAQ driver.
