PCI Express slot

Yes, it will be fine. You could even put it in a 1.0 or 1.1 slot.

Yes, pcie 1.0/2.0/2.1/3.0 etc are all forward and backwards compatible.

And... there is no noticeable difference in performance with any current graphics card.

PCI Express 2.1

PCI Express 2.1 supports a large proportion of the management, support, and troubleshooting systems planned for full implementation in PCI Express 3.0. However, the speed is the same as PCI Express 2.0. Unfortunately, the increase in power from the slot breaks backwards-compatibility between PCI Express 2.1 cards and SOME older motherboards with 1.0,1.0a but most motherboards with PCI Express 1.1 connectors are provided with a BIOS update by their manufacturers through utilities to support backward compatibility of cards with PCIe 2.1.