It's amazing how much things have moved on since the OP. PCIe is so versatile. NVMe SSDs are just PCIe devices, which are generally backwards compatible with older PCIe versions or reduced PCIe lanes.
I've successfully used these cheap vertical Cablecc adapters from Aliexpress to run PCIe 3.0 x4 NVMes in a PCIe 3.0 x1 slot:
(Similar items are available from ...
This is probably not going to work.
The mini pcie card can supply a peak power of 3.3V at 1A.
From what I can find an mxm gpu always needs more power than this and unlike a normal gpu it has no external connections.