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Well if you want to avoid screen tearing then normally you would cap your fps about 2 fps below the refresh rate, then turn on gsync in the control panel. Then you are always operating under adaptive sync. I haven't really noticed a difference between vsync on/off while running in freesync range so I just turn it off.
G-Sync should activate when you drop below 66fps, if you have both it and V-Sync enabled.
I would probably go with regular V-Sync for more performance intensive titles, ones where you are likely to be under 66fps a lot anyway, and Fast Sync for games like CSGO where you can easily achieve 2x max refresh framerates. With Fast Sync frametimes can get janky in the lower framerates
No, you generally don't want to use Fast-Sync. The only case where it's useful is for e-sports or old games, where you are getting over double the refresh rate in fps (e.g. 120+ fps on a 60Hz monitor).
If you have a G-Sync monitor (or compatible FreeSync monitor) just enable G-Sync, and select G-Sync as monitor technology (in Nvidia 3D Settings). Then force V-Sync On (in Nvidia 3D Settings) and disable V-Sync in game settings.
And, for the lowest input lag, you'll want to use RivaTuner to set a frame cap at 2 below your refresh rate (e.g. 58 on a 60 Hz screen). These are the optimum settings.