Keep calm and carry on

Answer 4 is both polite and clear.
Answer 1 remains slightly vague; Answer 2 misinterprets the word 'unleaded' ('un-LEDD-id', as in car fuel; not 'un-LEED-ed'): Answer 3 is too wordy.
'Leash' is a slightly old-fashioned equivalent word for 'lead' in this context.
Meanwhle you may have noticed that nothing is said about 'assistance dogs' (guide dogs for the blind, and equivalent trained dogs for those who are deaf or have other impairments).

'Alarmed' is a slightly strange (but reasonably understandable) way of saying, in a clear simple signboard, that the doorway is equipped with sensors and sounders, so that it will start up the sirens if anyone opens it except during a genuine emergency, such as a fire. We do also sometimes describe people, or even animals, as 'alarmed' ('My dog was alarmed by the fireworks next door'; 'Her parents were alarmed to think of her going to live with such a man') ~ so 'an alarmed door' does sound somewhat peculiar.

Answer 4, bizarre though it may seem, is correct. Let this be a warning to you about sloppy use of pronouns!

Such an alert during serious television news would need to be short as well as clear, so Answer 1 is the most likely. Answer 2 is grammatically sloppy; Answer 3 is possible but wordy (and may give viewers a moment longer to turn their attention elsewhere); Answer 4 means well but is not very tidy.

The final guided tour would set off at 4.30, but the doors are open for un-guided visitors until 4.40 pm.
(Please re-read the 'notice' if unsure as to why!)

Any of Answers 1, 2 or 4 would be more likely than No.3 ~ which is clear enough, for sure, yet somehow inadequately formal for this context with its serious concerns for public safety.

The announcement is indeed tantamount to a warning (as suggested in Answer 2), but that word in itself is probably regarded as too 'worrying' ~ so transport networks prefer to use the more positive and collaborative term 'advised', and then let their would-be passengers draw their own conclusion as to the seriousness and detail of the impact of the information.

Answer 1 appears to suggest that the carrying of children is compulsory ('What if you haven't got any?' as George Mikes once asked in comparable circumstances); Answer 2 is the correct one, saying that any such children as there are should be carried rather than riding the escalator directly themselves. Answer 3 is more colloquial than formal; Answer 4 is so weak and vague as hardly to be worth the cost of the signage!

There was an (unintended) pun on 'roll' in the original: the writer meant 'Don't break up your bread-roll into little floating chunks', but the instruction could be read as: 'Do not crumble your bread, and neither should you roll (yourself around) in the soup'.

Answer 1 seems clear but frightening (your author knows, from being startled by it, an example of just such a sign at a notoriously busy major-road junction not far from Oxford, and it may not be the only such one). Fortunately, if perhaps surprisingly, it is the wrong answer; No.2 is correct.
Answer 1 happens not to be wrong, but the primary meaning is as in Answer 2; Nos. 3 & 4 are not true.