catalog

I only know of having 1 single (production) recovery catalog database server, even in a multi-database and multi-host oracle db environment. you register all your (production) databases into that single recovery catalog, which shall have the highest version of any of the production databases.

technically, you could register your database in several catalogs, but I don't see directly in how far that could bring any added-value,if any.

in short: you only have 1 recovery catalog, and the backup scripts refer to the rman instance, which is the recovery catalog db.

I assume that you asking about a catalog database for RMAN.  Yes, it is usually best to create just one RMAN catalog database to manage the backups (and recovery if needed) for your other databases.  And yes, you then need to register each of your other databases in this RAMN database.

I do not understand what your last sentence means.

I mean..
I have a database B,
I want to know from there I want to know this particular database is registeres with another catalog database ----any command

From the recovery catalog you can see which databases are registered with it.  But, I don't know of a way to do the reverse: that is query to see if the database you are conencted to is registered with an RMAN catalog database, or not.

which query is related with catalog

please refer to the official documenation in that regards:
http://docs.oracle.com/cd/B10501_01/server.920/a96566/rcmquery.htm

If you have RMAN open (on the catalog server), the "list" command there will show you the databases that you have registered.

fine..