How are you getting on?

'Going off' (apart from 'moving away, as in the correct Answer 3) can also mean 'changing into a state of decay' (as in Answer 1), 'beginning to make a noise (or even explode)' (Answer 3), and 'change one's mind' (Answer 4) in the sense of losing enthusiasm for something.

In Answer 1, somebody is putting together (we might even say 'concocting') a story. All the other uses are vaguer and more metaphorical.

Answer 4 quite strongly suggests someone physically moving money from one pile to another ~ you can almost sense their arm swinging over. The other uses are once again much more metaphorical. 'Carrying out' (Answer 2) no longer means 'removing something physically', although 'carry-out' is the Scots equivalent of 'take-away' (as in buying hot food over the counter and bringing it home to eat); the only 'carrying out' from a fire drill might perhaps be when someone is injured and literally carried from the premises on a stretcher.
'Carry on' (Answers 1 & 3) simply means 'continue; keep going' (as in the newly fashionable slogan: 'Keep calm and carry on'); also, informally, it suggests 'to keep on with an affair' (i.e. a love affair; and hence the whole string of 'Carry On ...' films from many years ago; probably no longer a shining example, nowadays, for learners of British language or culture!).

There are some possible elements in the other Answers, but No.2 is the only one where both parts work acceptably.

'Grow over' may work in other contexts, but not with weather; plants may 'grow over' a patch of waste ground, for example.

Answer 1 was the mistaken one; if you reverse 'on' & 'off', it then makes good idiomatic sense. 'Getting off with' someone (perhaps now a somewhat old-fashioned term) means 'striking up a [potentially sexual] relationship'; 'getting on' simply means being on friendly terms (also, 'getting along'; with ~ perhaps ~ a sense of walking alongside them).

If you reversed 'down' and 'through', Answer 3 would then make sense ('cutting through an alley' meaning to take a shorter diversion between two places; and 'cutting down' the trees, though in a sense this would presumably entail chopping 'through' the trunks of them in a physical way).
In Answer 1, people can be (metaphorically) 'cut-up', i.e. psychologically raw and distraught, and they can cut down (or 'back') on something they would otherwise prefer to continue doing as much of as before.
In Answer 4, the idea of a person being 'cut out' for something suggests that they are metaphorically shaped for it, almost as in some kind of children's matching game; a 'cutaway diagram' schematically reveals the intricate inner workings of a system such as a power station, the internal combustion engine or indeed the human digestive tract.

Both usages in Answer 3 sound remarkably plausible but are in fact entirely made-up.

Another faintly plausible-sounding expression, yet it does not make any specific recognised sense. All the other expressions are fine: you may wish to check them in your dictionary, or one of OUP's 'English Idioms' books ~ try searching online for a copy, referring to Seidl and/or McMordie as authors).

Once again, all the other usages are standard; but in Answer 2, while there is some hint of an overall sense to it, these are not ordinarily recognised idioms.