There are multiple ways:
1. the inverter switch opens: the current will stop/voltage will rise.
2. the grid fails: a sudden jump in current. (you're feeding the entire street)
3. the grid islands: a sudden jump in frequency or power factor. This is also called ROCOF and Vector Jump.
It's very difficult to fool an grid-tie inverter. You'd need a 4-quadrant inverter for that. As far as I am aware, only Victron sells those that support islanding with batteries an grid-tied solar installations.
Yes, but what if I have exactly the amount of load? You need to match the exact load, including the exact power factor of 1. Grid tied inverter operate in power factor mode.
Any reactive current on your island will
not be supplied by the grid tied inverter.
One method is to stop the PV inverter for a short duration, and sense what the grid does during that short time. That works well for a stiff grid but has caused some grief for SMA users on weak grids or where other grid connected inverters don't like such 'glitchs'.
You don't even have to do that. It's enough to try to make a bit of imaginary current and measure if the real current lines up or not.
Yes, I'm pretty sure that's how it's done.
The standard 50549 does describe a resonant detection method but it does not go technical. I suppose you could do that. You cannot interrupt power because you'd be injecting harmonics.