First I would suggest checking your signal levels. DOCSIS 3.0 requires tighter restraints to the signal specs. Another words, a signal problem that might not have caused a "symptom" with your old D2 modem might be giving the newer D3 modem issue. You should be able to find them at 192.168.100.1. But to answer your questions;
1. You can't.
2. No. It requires that you be using the modem that your trying to register.
3. Not that I have seen. The instructions are given during the registrations process.
4. Yes.
The self activation system detects the serial number and MAC address of the modem your using during activation. What it requires of you is your account number and specifics. It's mainly designed for people to be able buy a modem and start service without having to call Cox. It sometimes has problems swapping equipment, especially if your going back and forth. Your better off calling Cox up from your cell and having the representative add over the phone, that way they can see your modem come up and confirm the signal levels.