Erm... Americans have states, Britons have counties, Russians have oblasts. Yekaterinburg is its capital, Koptyaki is within its borders. As for the claimants -- they are everywhere... there was a couple of Alexeys IIRC.
Well, Anastasia was shot along with her family, if we are to believe numerous accounts of eyewitnesses and invesigators. The statements concerning the immolation of two of the Tsar's children and the existence of four very similar jaws have pretty much finalized it for me. Of course, miracles do happen... but this is too much.
I would like to reiterate it again: it is unwarranted not to have doubts.
Erare humanum est! Also, it is unwarranted not to doubt that Anna Anderson was Grand Duchess Anastasia, if we are at it, because there is no scientific evidence that upholds her claim... none at all.
As for your correct statement that she knew things NO ONE on the outside could have possibly known -- it implies that someone among the insiders could have known. Possibly she was very well-trained by... my my, I have to stop as I am not into conspiracy theories!