There used to be a kind of convention of companies using ssl.example.org style sub-domains (as opposed to www) for these. IIRC ebay did it in the mid 2000s, and some others as well. I have not seen any research, but I've worked at a large e-com company that did that too, and explained it with copying from even bigger companies, because if they thought it was right it must be.

Why do you think that's bad?

In the US a private customer typically does not care about the billing address. They just want their stuff. In Germany for example we like the billing address, and typically would want our stuff shipped there, so it's common to ask just for the address and then ask for a different shipping address.

I like what booking.com does. They have one text box, but the display inside that box changes depending on the type of card, so they will break it up into 4 blocks of 4 for VISA or MasterCard, but behave differently for e.g. Amex. You can paste one long number into it, and it looks really neat.

Those guys over at VIES also have a free API that can validate VAT numbers as well as company information, or find them.

Actually it also depends on whether the invoice is the symbol of going to the step of paying, or if it is one payment method (the one where you get an invoice and pay later through e.g. transfering money) among others (which could be creditcard, paypal or similar).