Wouldn’t it be fun?

'Should be' (Answer 1) explains the situation almost from someone else's, administrative, perspective (i.e. 'According to the rules / my contract / what my parents told me ...'); 'might have been' suggests an opportunity already missed, and perhaps regretted ('Had it not been for my accident, I might have been playing in the Final this afternoon').
'Ought to be' recognises an obligation, but it also contains a definite sense that the speaker has other priorities (e.g. that it's more enjoyable staying on at the party; that their homework, or tomorrow morning's duties, are not so important, etc.).
'Ought to have been' (Answer 4) makes it even clearer that it's too late to make the move by now; that the speaker has perhaps missed their last bus/train/ferry.
All in all Answer 3 is probably the most likely and natural.

'Would' and 'should' are stronger than the other two Answers; but 'should' carries a slight suggestion that the writer feels obliged to take an interest ('should = ought to'), whereas 'would' retains a sense of voluntariness (i.e. wishing or wanting; a personal, individual, quite possibly partly emotional interest).

'I couldn't care less / couldn't be bothered' etc. is a (sadly!) widespread expression.
Picking it apart, it means that the speaker would never be capable of taking any less interest in something, i.e. their interest level is already 0% and there is no way that this could be reduced further.

Open any suitable secondary maths textbook or website, and sooner or later you will find these words somewhere!

Answers 1 and 2 are probably too strong; how do we know that the person giving this opinion, themself knows that the advertisement contains (at least, some) untrue 'information'? (Unless they are behind the writing of the advertisement in some sense, like they work for the company that makes the product, or actually on the advertising campaign!)
'Can't' suggests that they know, or think, that nobody else is capable of accepting every claim in the advertising; 'mustn't' suggests that they know of factual (or maybe moral) reasons why nobody ought to trust it; or they might just be being cynical about advertising in general (rightly or wrongly ... this is not the appropriate forum to judge that point!).
'Shouldn't' strikes a tone of strong advice rather than trying to tell anyone else exactly what to think; 'mightn't' (Answer 4) is almost too weak an argument or recommendation to be worth bothering to express.

As the saying puts it (in another sense of the word), 'Might is right' here ~ because at the time when she told us, she wasn't yet sure whether or not an earlier train would be possible. 'Would' (Answer 1) would itself, therefore, be a little too definite; 'could' would be understood, but is not the most natural way of putting this.
The phrase 'might is right' is used to summarise the argument that the physically strongest, or most numerous side will win, irrespective of whether their cause deserves to win. 'Might' here means 'strength' (more usually found in its adjective 'mighty'). We might [!] regret that many users of English are not bothering about some of the details being correct; but if enough people don't bother, then the wrong/sloppy use will become the accepted norm (i.e. 'might may become right' ... even if what they say or write is still technically wrong).
Apparently there was a propaganda campaign in GB during World War 2 whose main slogan was 'Defend Britain with all your might' ... and research discovered that many people believed this meant that they 'might choose to defend their country, or they might not', so that particular campaign was discontinued. How awkward that two uses of the same fairly common word should have such seemingly contradictory meanings!

'I would not be surprised if he did ...'
(This is, we suppose, a Passive Negative Conditional ... but it's ever such a natural expression to know and use.)

'Had it been sunny, we would have eaten' is the basis for this, but the additional choice of a Continuous construction emphasises how this alternative would otherwise have been happening at this very same moment (in an alternative universe ... where the English weather was always perfect!).
Answer 3 is possible but less likely or strong; Answer 4 is wrong twice-over because 'may (or 'might') as well have ...' suggests there was still another just-as-good option (which in fact has been denied by the weather); and 'of' instead of 'have' is a frequent mistake even among native-speakers (what with its similar unstressed pronunciation) ~ but it simply doesn't make grammatical sense, even if its apparent meaning remains otherwise tolerably clear.
You may wish to check on the vocabulary for all these words with the short 'u' in them: 'tuck in' (slightly slangy; and it does have another meaning, as in 'tucking someone into bed'); 'fuggy' and 'huddle'.

If the delays are definite, there is no responsible sense in pretending otherwise!

'May' would have suggested, perhaps, around a 50% probability; the shift to the conditional suggests that chance is further reduced, maybe to a 25% or 33% level or indeed less than that. As modal verbs go, this is the one that a motorist would be (relatively) happy to hear, and would set out reasonably confident that the remains of the accident (and backed-up traffic) could more than likely be clear by the time they reached the relevant junction.