There are prepaid cards in almost every US grocery and convenience store, typically Mastercard and Visa. They don't require any ID to buy and have a fee around $5. Most can't be reloaded.
You can exchange bitcoins on IRC for prepaid virtual visas and mastercards, paypal, any 3rd party payment you want. There's a few web services for exchanging coins to visa too, which I can't remember right now but are posted to bitcointalk forums.
Of course if you were setting up an illegal hidden service payment would be the least of your worries. Moving it around every few weeks inside Russia like the inter-dimensional dark fortress in Krull to prevent long term traffic analysis, maintaining your site from a moving location everyday, and making sure you don't blow opsec giving away your identity is probably more difficult than finding creative methods to pay for hosting.
They all do (maybe not Diners, I didn't realize they were still a thing). I use them from time to time to get around the geofencing of purchases, or when I really don't trust the site.
No, Direct Deposit in Germany usually refers to Giro[1] which is a payment between bank accounts. (Credit cards and even debit Visa/MasterCards are relatively uncommon in Germany)
I've never seen an actual cash deposit payment while I lived there, though we do have them in Sweden for example.
Seems like that should also open one up to an identifying attack of sorts. Find out when deposits were made (assuming there is more than one), grab all the security video from those times, and try to identify the person who is in all of those clips. Facial recognition software should get one the rest of the way. I imagine you would only need 3 or 4 deposit events to reliably identify someone?
[1] http://www.hetzner.co.za/helpcentre/index.php/articles/conte...