What requirements are needed to open a EU bank account?
Getting a bank account isn't really easy.. but you can get prepaid cards that have their own IBAN (essentially bank account number) attached. The accounts have no name but you can put whatever name you want on the SEPA/wire transfer and it will be credited just fine. It's a proper anonymous bank account. Wire money, withdraw from an ATM.
Any of these will do;
http://allegro.pl/listing/listing.php?order=m&string=visa+prepaidIt's probably best to get the EUR denominated ones since they will work with SEPA rather than SWIFT (actually you can use them all with SEPA, but SEPA is EUR only so there will be fx fees if it's a non-EUR card).
They have a low yearly limit per card, but the cards are only like $5 so you can just get a few of them.
allegro is a Polish ebay site.. it's a bit hard to navigate if you don't speak Polish but it's doable with help from google translate. In order to actually pay for the auctions it uses a polish paypal clone called payu.pl. It's a bit tricky to sign up to that too but it is possible even without any polish identity or address. You could also try contacting a seller directly and asking to pay by paypal or some other means.. maybe some will even take bitcoin.
Another option that many people don't realize is that btc-e.com allows withdrawing money to any visa card.. including the ones already in your pocket - and it probably works with most prepaid visas you can source locally too. It sends the money through the visa network (using the long number on your CC) so it doesn't require any bank account to be attached to the card.