Oracle - Need help with RMAN Active Duplication on Windows 32 bit to a 64 bit
You have to initiate the duplicate from the target database to be able to connect to the not mounted target database. I suggest you to downgrade the oracle version on the 64 bit machine. The easiest way to do this will be to install 11.1.0.6.0 version on the 64-bit server into a separate oracle home and perform the duplicate.  You can upgrade the database  after duplicate and switch it to the 11.1.0.7.0 home.   

The error you are getting on the 32-bit database seems to be  a connection problem to the database. The target instance is not mounted and you cannot connect to is via SQLnet.

When performing the duplicate form 64 bit system, please make sure that you are using username/password in the connection string to the target database and not the system authentication. 

Best regards, 
Yuri