You need a SAML stack for your application.
Refer SAML : SAML connectivity / toolkit and the links in that entry.
For A, perhaps you can use the WIF SAML extension mentioned in the article above?
For B, you need to rip out the DB authentication and add the SAML functionality as for A or else have a look at Identity Server which you can federate with ADFS and which also authenticates using a DB (but doesn't support SAML itself).