Can I use a credit card or electronically buy a gift card? That way I wouldn't have to wait. Will Airplay work with the Apple TV the same as it does with the US store? Looking it up, it looks like you need a mailing address in the country from which you're buying. How do I get around that? Can I just pick a random address I find via Google? I doubt Apple really checks everything like that.
Is there a way of buying a German itunes card code so I wouldn't need to wait or pay for shipping when all I need is the code?
As far as I know, you have to do the gift certificate trick, as the credit card has to have the same nationality as the store you want to use.
Just find a random address in the country you wish to use. I'm sure Apple doesn't really care, the still get paid. I think this restriction is part of their agreement with the studios who still think we live in the 1980's.
It doesn't matter what e-mail you use, just as long as it is not connected with another Apple ID.
The way it normally works, when people buy american gift cards, is they buy them on eBay for example, then the seller just emails the redeemable code, so there is no need for shipping or waiting for the mailman
Does Apple TV have the 90 day account switch restriction?
There are lots of thorough tutorials out there, just search for "how to make an iTunes account for another country".
I'm not aware of such a restriction. I never change my account on the ATV, only on my iDevices.