These inverters have to switch off if they cannot detect a grid signal, or if the grid frequency/voltage goes out of the safe range.
Same legislation as the non-plug&play inverters.
Same legislation as the non-plug&play inverters.
Some models of inverter brands like Victron (which isn't very common outside its niche of self-sufficiency because they are rather expensive and sometimes complex) can form a micro-grid. They have the option of a special circuit breaker [1] that decouples the inverter from the grid if the grid is detected to be down, which allows their use during a power outage.
[1] https://www.victronenergy.com/accessories/anti-islanding-box...