Answer 2 is pretty much the whole point of an "isolating" transformer. It isolates.
And no, there is no voltage between either output and ground (except for the leakage current, which, for an 'isolation' transformer is designed to be 'too small to matter').
There is voltage between the two contacts of the output transformer. That does not mean there is voltage to ground.
Since this is a NZART exam question, you can be pretty sure that they are thinking about the high voltage (AC) output of a radio transmitter, both in test and in use.
That explains the wording of the answer: 'touch'. The danger is that you, or someone, might 'touch' the high voltage AC output of the transmitter, or that it might 'touch' something like your iron roof, and make it live.
Yes, an 'isolation transformer' isolates the inputs from the outputs -- so you can hold one of the inputs and one of the outputs at the same time if you also have an isolated input. But that is not the ordinary use case. Ordinarily, if you already have an isolated input, you don't need another isolation transformer.
The ordinary use case is that you do NOT have an isolated input. At least one side is live to 'something else'. The case, the signal ground, the ac ground, neutral, whatever. As it happens, almost always your non-isolated input is not isolated from 'ground' and other non-isolated elements are also not isolated from 'ground' so even if what you really need is isolation from 'conducted interference', that means the same as 'isolation from ground'.
The other main use of an 'isolation transformer' is to isolate "things" that are different potentials -- for example adjacent buildings connected by ethernet cables or telephone lines -- and in that case, you may deliberately connect one side of the isolated output to ground. It's not isolated any more. But the isolation transformer has done it's work of isolating from ground so that you can connect either side (or any point) to ground.
We aren't all radio engineers, and an isolation transformer will create a floating output that is safe in the presence of one (1) ground fault. You can touch either side of the output, and it's safe, because it was isolated from ground. This may be a DC voltage (solar panel) or an AC voltage (test equipment, or equipment under test).
But the answer is generically true even for cases that don't involve the expectation of 'touch'