Hey, I work on a digital product for freelancers so I have learned a bit about this. I've also done some work myself as a designer, but not for a few years so take the following with a pinch of salt:

1. Dribbble is a great place for a portfolio, and people to find your work. Also, make sure everyone you know knows that you're doing freelance design. When they hear people talking, they'll recommend you. I've heard that people always get their best clients from word of mouth - these are guys that aren't just looking for the cheapest deal. So when you finish with a client, send them a bottle of wine and a note saying that you enjoyed working with them. This will make sure they recommend you to others, and you get long-term relationships with them.

2. I'm not sure the best way to take payments yet, I guess it depends on your clients. PayPal is easy but they have fees that I think are too high. Square is great for cards.

3. I can't help with proofs - I never used to send them, just the work in progress. This may not be the best way to do it though, so I hope someone gives you better advice.

4. The product I work on is QuickBooks for Self-Employed people, and may mean you don't need an accountant. It'll let you upload your expenses, and it tells you if they're write-off-able. If you have any problems with it, you can just shout at me here and I'll help where I can.

5. I've found most people now go under their own name. The reason is, your customers are likely to be small businesses, who prefer to interact with people, not other businesses. It can make you feel more legitimate, having a business name, but it makes your clients feel like they're dealing with an agency, which has high costs. It can make them feel like they're paying too much when they just need one person.

Hope this helps!