Yes, you can connect a GPU with a PCIe to a Mini PCI adapter.
Yes, you can connect a GPU with a PCIe to a Mini PCI adapter.
Yes, you can connect a mini PCIe device to a mini PCIe slot on your PC and use it for a graphics card.
Yeah, but you'll be limited to x1 which will severely limit performance (if you even find a GPU that will run at x1).