You can use your normal Amazon account/login, but prime benefits don't transfer.
Yes, you can use your normal credit card. You can pick whether they bill you in USD or Euros.
No import duties that I've noticed, but I've only put through orders up to $500.
WRT pricing, the prices on Amazon.de include VAT, but they remove it when you get to checkout. That usually covers most of the shipping costs in my experience. The biggest issue I've had is the time it takes to get them to your house. If you don't pay for expedited shipping, it can take 3 weeks or so and the tracking isn't great. That said, Amazon has taken care of any issues I've come across.