At 1080 you aren't using HDMIs bandwidth up. The exception and why many might say to use DP and id be inclined to agree is HDMI cables are not all created equal. There's 2.0, 2.0b, 2.1 (which now includes 2.0, idiot HDMI organization), and length limitations to further complicate it.
To the point of you "might be getting 180 but not" is misleading but valid. You could be getting 180hz with no issues or with intermittent issues, or you might not even notice issues if there are any. It's a preventive weed it out before it's an issue solution.
Free-Sync should always be on. It eliminates tearing and stutters whenever there is an FPS dip, basically real time compensation. G-Sync is Nvidias's proprietary FreeSync. Oversimplification; Think of it in HDR how DollyVision sits on top of HDR. All DV is HDR but but all HDR is DV. Same goes for Nvidia, all G-Sync is FreeSync compatible not the other way around (however some are G-Sync certified vs compatible, different rabbithole).
FreeSync is compatible with your monitor, I did find it odd the manual didn't mention if HDMI and DP and would carry but assume it's both? Not sure if that first bit above was you asking or saying what your research turned up.
Either way FreeSync 100% on.
We are all new somewhere in life so ask away. Can't guarantee I'll be able to answer it all but in life it's always better to ask even if it possibly makes you look silly or annoying than to assume and be wrong (and depending on the topic, irreparably destroy the subject in question).