Why was Gryffindor's sword in Bellatrix's vault?

I'm wondering something and can't put my mind of it. It's years and years ago since I've last read the books, so maybe I've missed something, but...

When Harry gets captured and taken to Malfoy manor, Bellatrix freaks out when she sees the sword of Gryffindor. We know it is because voldemort ordered to keep the cup, which is a horcrux, hidden in her vault. This is all this obvious, but now my question(s).

The sword, even though it is a fake, is also in her vault. But why did she hide it there? How could voldemort have known that the sword had absorbed the snake's venom and so it was capable to destroy the horcruxes? Or what would be another explanation why the sword was hiding in her vault?

Snape probably gave them the fake sword, but did why? If it was to gain trust, he had given it before killing dumbledore. Did he even know of its capabilities, because how else would they know if he didn't tell voldemort?

I know that are a lot of assumptions and questions but could someone clarify this with a broad explanation?