From my understanding, the PSQL v9 client has not been tested and is not supported on Windows 7.
Will it work? Maybe. You might want to look at the Vista whitepaper since Windows 7 is similar to Vista.
Can you use the v10 client with a v9 server? Again, it's not tested. It might work from a Btrieve perspective but I would expect problems with the ODBC / SQL side.
What issues are there with moving the application to v10? Upgrading to v10 gets you full Windows 7 support and support in general.