Hi Vikas,
Have you tried configuring 64-bit ODBC DSN of Postgres database, where BO server is installed?
As Webi Processing Server is a 64 bit server, it is looking for the 64-bit ODBC connection, while opening & refreshing the report.
Create a 64-bit ODBC connection with the same name of your 32-bit connection on BO Server machine & then give a try.
As far as Postgres Database support for reporting is concern, I believe it is supported. You can check the supported platform guide of BI 4.2 Webi from SAP's Help portal under Additional Information section.
Thanks,
Shailendra