BlurBusters is a good resource for monitor-related stuff, however they're extremely technical and so you can leave with more questions than when you started. Here's my summary, but I can go into more detail if needed:
FastSync and G-Sync are compatible, because they work in different ways. FastSync is a GPU feature that caps your framerate to your monitor's maximum refresh rate, and then drops extra and unfinished frames to help reduce screen tearing. G-Sync is a monitor feature that dynamically adjusts a monitor's refresh rate to match a game's current framerate when it drops below the monitor's maximum refresh rate, reducing screen tearing. In other words, FastSync works on the upper end of framerates, while G-Sync works on the lower end of framerates.
Using both technologies is likely okay for almost everyone, except for twitchy shooters, in which case I'd turn off FastSync and instead just cap my framerates via the game's cfg file, to a manually optimized number based on things like my framerate lows/highs in that specific game. Also on that note, G-sync wouldn't be necessary in a game that has consistantly high framerates since the feature automatically disables itself whenever the framerates go above the monitor's maximum refresh rate--if you have a fancy G-Sync monitor, it's not helping you play Counter Strike Go with 600 frames per second, as the G-sync feature is disabled in that case. FastSync would do something though, and it would cap that 600 frames down to 240 or whatever the monitor's maximum refresh rate is, while working to reduce screen tearing too.