Can this phone be programmed to auto-dial a SIP address instead of a regular phone number?
Yes, you can. Please refer to the IP manual (UP 3)
If power or internet temporarily fails, will the phones still auto-dial correctly when restored, or do they need reprogramming?
Yes, all data is stored in non-volatile memory, so all data will be saved.
Does it need PoE? Can it run on 12 V or other standard power?
Yes, you can choose your power source (PoE, 12V power supply).