These and Those - Demonstrative Words

The 'people' are plural, which narrows the good answers down to (1) or (4). But if, in Answer 1, the people are nearby ('these'), so will the noise be, so it should be 'this noise' rather than 'that noise'.
In Answer 4 we have plural people and a singular noise, but both of these things are at a distance ('those ... that').
Most languages, for obvious communicative reasons, have ways of defining nearby things and ones that are further away. Think of the pair 'voici/voila' in French, and phrases like 'koko ni' in Japanese.

'One of those days' is an expression that means 'a day like THAT', i.e. the sort of (bad) day that you don't want any more of, so you would use 'that' or 'those' to suggest that you want to be distanced from such an experience. If there have been a lot of bad days (or you fear that there might be), they would be both far-away and plural, which is why you say 'those'.
The other expression is 'THESE days', meaning 'recently' or 'round about now' ('Grandmother isn't looking so healthy these days.'). We say 'one of these days' to suggest that a thing will happen quite soon ('One of these days he'll realise what a fool he has been.').

The documents are (a) plural and (b) somewhere near to the person who is speaking, so 'these' is the only right answer.

'Instructions' are plural, and we may assume that the warning and in instructions are printed nearby to each other (it would be unreasonable if they weren't!): so, 'these'.

If the first car is 'here', it must be 'this'; so the other one is 'that'.
You can't really have 'this ... and this' in the same sentence (though sometimes it does make sense).
'These' and 'those' refer to plural things, and one other car can't very well be plural.

'You (over there) do it your way, like that; but we do it our way, like this.'

The first plug that's mentioned is singular (' ... is ...'), so it must be either 'this' or 'that'. The sentence then goes on to refer to other ones that are different (which must be 'those': plural, because this is one among many).

Churchill hoped that future people (like ourselves!) would be able to look back and say 'THAT was their finest hour'; but at the time he was speaking, the difficult hour was close upon the nation, so he said 'This ...'.

We assume that the magician is holding the cards near to himself and drawing your attention to them; and that they are plural (so you can make a choice of one of them); so the first blank word must be 'these'.
On the other hand, there is only one box mentioned, and it is further away ~ the distance may be some part of the trick to come ~ so the only good word here is 'that'.

'There it is, the question': 'That'! (Almost everyone who knows any English at all has heard this famous quotation.)