For a relay snubber to protect your circuit from inductive kick spikes in the audio which happens when you disconnect power to a relay which has a pull in coil inside, the diode should have a reverse voltage that exceeds the voltage that the relay coils run on. This will usually be 6, 12, 24 or sometimes 48 volt relays. A 1N4148 is a common choice, (75 volt PIV-peak inverse voltage) as is the above mentioned 1N4007, which has a PIV of 1000 volts.
The 1N4148's are half the price of the 4007's.
The diode is usually wired right to the relay. You must observe polarity. The cathode, or stripe on the diode, should go to the positive side of the pull in coil power pin. This is a reverse bias setup. You do not want to forward bias the diode, otherwise, it will conduct current and short out your pwr supply.
The spike induced in your supply line is opposite in polarity to your pwr supply, thus, the reverse bias. Some folks put a cap/resistor snubber in there as well.
I am not sure about your reg. protection diode, so I will let someone else take that question.