Generally speaking, most if not all hardware running Win 10 will be able to work on any Linux distribution making a few exceptions where external drivers can be found. Normally though, this will not be necessary as it will be pre baked into the kernel with no interference from you
That being said - Mint runs an older version of the kernel compared to the current state of desktop Linux and may not contain certain drivers for hardware that came out after that specific kernel version was released. You can use a distro that favors being up to date over long term support, such as Fedora or Arch (if you’re willing to put up with setting up Arch) if that crops up. But generally, if you’re running win 10 still this shouldn’t be a problem
Without knowing your hardware, i can’t really say more though. Just try mint or any other distribution on a live usb and if it works there, then it will work when installed
The 580 legacy driver is DKMS, so there shouldn’t be any maintenance beyond what is already required for any other DKMS driver, which would be handled by pacman anyways. So no need to worry about kernel updates
If you’re adamant on keeping those GPUs, Nouveau would be the only path forward - eventually paired with NVK for Vulkan acceleration once that’s good enough for primetime. Pascal was dropped because of the lack of a GSP module as well as age, so the newer Nova driver won’t support it either