Problem #1: Have you tried disabling the Auto-Answer/Receive option when using the phone?

Problem #2: Have you tried adjusting the number of rings between the time the answering machine picks up, and the number of rings before the Fax picks up? It's highly likely that both the answering machine has the adjustment, and I know the fax machine does, so you might try going into the menu to see if you can get the desired result by either adding more rings to the fax machine, or less to the answering machine.