Pretty much any landlord would bite your hand off. If you find something you really like and you have enough cash, perhaps think about paying a lot up front (6-12 months) so that you can negotiate a better deal. Plus you might be able to get a bank account if you find an agent with a very good relationship with a branch manager of a certain bank. Good luck
No it's not normal, but I hear that it's a somewhat common alternative to be given a tourist visit if for some reason you didn't qualify for the DTV. You could question it with them, but I doubt it's a mistake
There will be several agents who claim that they can do that for you, and some actually can, many for a high fee. But I wouldn't bother at this time, even if you get a bank account, it could be closed / frozen on you at any time. I'd wait until the laws change