Oracle DBA jobs are related and Conditional of knowledge of some of the other Oracle products Like Oracle Application (E-Business , CRM and others). Although that is not related to the functions of DBA job. my Question is: is this is the right way for hiring the DBA ?

Yes. The entire Applicaion Data is stored in Oracle Database therefore an Oracle Application DBA is also a Core DBA in EBS environment.

NO,SQL DBA Optimizer, on which any application you develop is going to depend.

application dba as one that runs SAP, Peoplesoft, Oracle apps -- they are definitely "in production"

Oracle DBA and Oracle Apps DBA are 2 different positions. It is good for Oracle DBA to know Oracle Ebiz. Database and Schema.

Generally Oracle DBA should be strong in Oracle Database, Not necessary to know Oracle Applications Database tier.

Oracle DBA can take up positions in Non Oracle Applications even as long they are using Oracle Database. For example Application front end can be any other, but the backend database can be Oracle, if it is portable.

Yes Oracle Apps DBA should and must know Oracle DBA Task.

Yes they need to have some knowledge in oracle apps, this will help them in extracting data and fine tuning

Yes they shall have atleast overview knowledge about all the oracle apps as they need that to extract data corrctly