Nobody's Problem - Possessive Apostrophes

Presumably, the jacket belongs to only one brother. If there's only one owner, the possessive apostrophe goes INSIDE the word, just in front of the -S rather than on the back.

Answer 2 is most probably right, unless more than one person was sitting on just one horse (i.e. 'plural ownership of a singular thing') ... in which case, no wonder the poor animal was so exhausted!

Even though this is a Possessive use, there is NO apostrophe in 'its' (= 'belonging to it').
Of course, you will often see an apostrophe in 'it's' (Answer 2) but here, the apostrophe is doing another job, showing that one or more letters have been left out ('It's a lovely day' = 'It is ...'; 'It's stopped raining' = 'It has ... ').
Answer 3 is simply wrong; it looks as though it is trying to express plural ownership (as in 'The players' delight when their team won') ... but how can 'it' have been plural in the first place?
The shark may happen to be male, but surely people are more concerned with the front end of it (i.e. the approaching teeth!) than whether this fish happens to be male or female, which you're unlikely to be able to tell from the front.

'Women' is an irregular (if very common) plural form.

'Traffic' is an un-countable singular thing, so the apostrophe comes inside the word, before the S.

In this (fairly common!) case, 'children' is an irregular plural form that doesn't end in the usual -S; so the usual rules about dealing with S and/or an apostrophe cannot really apply. There is no such word as 'childrens', anyway ...

Only one 'Dad'; and when we need the possessive form of a name that ends in S, we can either just put a single apostrophe after it (as in Answer 4), or some people prefer to put another S as well ('Jones's butcher's shop'). Many English people feel that is rather fussy, particularly if the name has more than one S in it anyway (as in 'Jesus's parables and miracles').

Answer 3 is most likely, assuming she has more than one neighbour (so that they are plural). If she only has one neighbour, she must be doing an awful lot of spying! The outer two answers (1 & 4) are each simply wrong.

There is only one England, so it is singular and follows the usual rule!

Answer 1 would have been possible if there were only one bear (but that wouldn't be such fun!); the correct title has several bears, so they are plural, with their apostrophe on the outside.