Yes, you can operate the graphics card on a motherboard with PCIe version 2.0 without any problems. The card is designed for PCIe 3.0, but is backwards compatible with PCIe 2.0, so it will also work there. A noticeable loss of performance through the use of PCIe 2.0 is hardly to be expected with this card in practice, as the GeForce GT 1030 does not require a very high bandwidth.

The maximum digital resolution of the card is 7680 x 4320 pixels, which easily supports your 34-inch UWQHD monitor (typically 3440 x 1440 pixels). You can therefore fully utilise the maximum resolution of your monitor.