Reading an old story, I have some problems with understanding the following (esp. the part in bold):
it was this very day fifty years ago—February 13—the man disappeared
from its shadows; swept in this extraordinary, incredible fashion into
invisibility— into some other place.
My understanding (using simpler words where I am more certain about the meaning):
…abruptly carried away, in a very extraordinary and incredible fashion, so that he became invisible and got into another place.
Is that correct? I have particular problems with understanding of "into invisibility".
Yes, you understand it correctly. "[he was] swept into invisibility…" means he became invisible. The author uses "swept into", which distributes to the two conditions in apposition: invisibility = some other [unknown] place.