A. Normally no, the BDC shares a common SID with the PDC of the domain and so there is no way to move a BDC to another domain, you would need to reinstall the BDC.
System Internals have released NewSID 3.0 ( from http://www.sysinternals.com) which has a SID-synchronizing feature that let's you have one machine copy the SID of another. This makes it possible to move a BDC to a new domain. On the BDC start NewSID and click "Synchronize SID", enter the name of the PDC and click OK.