1. Looking at the PC specs, you should be okay with any single-GPU graphics card upgrade. The things you need to know for video card upgrades are power supply (in this case, 480W) and interface bus (PCIe 2.0 x16). The only potential problem here is if the particular power supply used in this machine is of low quality and either has problems delivering its rated power or has a weak 12V rail; to find this out, you need to know the brand and model of the power supply.
2. Any monitor is okay with a modern graphics card. Most (all?) graphics cards support higher resolutions than any single consumer-level monitor can even display, and have dual-link DVI or HDMI connectors to provide the necessary bandwidth. The most common connection for modern desktops and monitors is DVI -> DVI, but you can use VGA-DVI or HDMI-DVI adapters also. In short, don't worry about it.
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