No, pci-e is backwards compatible. You won't hurt a 3.0 card putting it in a 2.0 slot.

You can run three cards on a motherboard, probably, but I don't think you would want to mine with it. Two won't have any room for cooling, so they will get exceptionally hot. It takes exceptionally loud external fans to cool 3 GPUs stacked on each other like that.

I would instead run two, so that the top card has some room to breathe.