Map PCIe slot number (or BDF) to device number or vice versa

What should be: The PCIe spec states that all slots start at 1x/v1.0 and negotiate how many lanes they can use and what clock speed. It shouldn't matter which supports more lanes/clock, some slots are designed to take larger cards and smaller cards fit in larger slots. Whatever the highest spec both sides can communicate at (both the number of lanes and the clock/version), that is the speed that will be negotiated and used. Endpoints can support 1x, 2x, 4x, 8x, 16x, and 32x, though there are no slots specifically for 2x and 32x. Speed is specified by major version number (2.5, 5.0, 8, 16 GT/s).

What really is: Usually what should happen is what actually happens. But there are quite a few boards (especially enthusiast boards) that do not follow spec. Some motherboards will not use anything but a 16x video card in their first PCIe slot. Others will not auto-negotiate correctly (commonly falling back to less lanes - this seems particularly common with 2x cards that negotiate to 1x speed). In server grade hardware these problems are very rare, but it happens. If both the system/motherboard are from the same manufacturer as the card, you should be able to contact their support and find out if it's a supported configuration (if they don't know or can't answer it's a huge redflag and you should consider not buying from them/returning). Also, try searching your particular motherboard and see if anyone has reported a problem.

I understand your logic in going with a USB 3.0 PCIe card over the integrated USB 2.0 slot... But this is still a pretty bad idea. Unless you're installing "HyperV Server" (stripped down with the minimum features for a hypervisor only), it may even be near useless if you can actually get an OS install to work.

USB drives don't have device access times that you'd need to get anything resembling reasonable performance for an Enterprise production environment.

Perhaps try a consumer grade PCIe SSD?