This is a side point so sorry to hijack, but I think there should be a 'mobile midwives' service associated with each hospital for this kind of situation. It is silly to me that an ambulance is often the first port of call when Ambos don't have specialist training (there was a great article on this in the Age last year so I'm being Victorian biased).

If it were me:
1. I would call one of the midwives I know or the hospital to ask what to do next.
2. The form depends on whether you go to hospital or not. If not then you can get a GP to sign a stat dec saying you had the baby and to help you register the birth.
3 I would always opt for post natal care even if its a day or two after the birth. It could be hospital a midwife or a GP who can do a home visit.
4. I would have blankets towels and clothes for baby.
5. Don't touch the cord. There is no need. The placenta will come out and then you can cut it when you get some help or get some advice.