That is correct. Unlike a normal Transformer which has two coils primary and secondary that are not electrical/physically connected a Variac only have a single primary coil where it's output is taken from, with a common neutral point, the output of a Variac is not isolated.
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Most Variacs have a few "extra" windings. So the output will be higher than mains. Usually around 17%.
Yes correct, that's the built in boost features, it comes in handy for testing most baseline smps application with slightly higher voltage above 230V.
A variac does not have the all properties of normal transformer because it cannot achieve the physical isolation between input and output.
That is correct.
Unlike a normal Transformer which has two coils primary and secondary that are not electrical/physically connected a Variac only have a single primary coil where it's output is taken from, with a common neutral point, the output of a Variac is not isolated.