I've done independent PDN in the past. My advice may be a bit outdated, but here goes:
1. I got patients through referrals: through contacts at hospitals, doctors' offices, and general word of mouth.
2. Be careful about taking on a case that you've worked with before through an agency -- there is very likely a non-compete clause in some of the paperwork you've signed. I'm not saying this can't be done, just that you need to make sure you're on the page with the agency requirements.
3. Billing is tough, and, frankly, I wouldn't recommend that someone do it. What I did was bill the clients (or their families), provide them with an itemized receipt, and let THEM file with their insurance provider. Of course, that means they have to put up the money up front, but the alternative is your providing the money (through your services and time) up front.
4. There are a couple of options for health insurance: an individual policy through a private agent (expensive, but costs can be kept somewhat under control if you opt for a sky-high deductible), by working part-time at a facility that provides health insurance, or -- as I do, because we are all in excellent health -- self-insuring. What "other" insurance are you thinking about? If liability is a concern, I don't recommend it (which I've covered many times on here, as a search of the archives will certify : ) but buying it is not a big problem: grab a copy of any journal, and there should be several ads there, and the costs are usually around $100 per year. An internet search would probably give you roughly the same information.
Jim Huffman, RN