if it's a PCIe 2.0 slot, then it will fit a card which supports 3.0. As far as I know there is no card which is ONLY compatible with PCIe 3.0. Most of them, most high-ends, are PCIe 2.0 + 3.0 supported. But you will need an Ivy CPU to make use of the 3.0 anyway.
So, a PCIe 2.0 x16 slot will be able to handle the new cards which come with 3.0 as well.
yes a pci-e x16 slot can take in pcie cards of any size
pci-e 3.0 is just the generation to which it belongs...it is just the latest bandwidth standards and has got nothing to do with its connector size.