'An' is before a vowel sound, 'a' before a consonant.
An apple, an orange, a banana. But also an hour, because that sounds like a vowel.
Apostrophes can be for possession - as you say, mum's is belonging to mum.
If it's a plural possession, like 'the ball belonging to the boys', it goes after the s:
the boys' ball
If it only belongs to one boy, it is before the s:
the boy's ball
Apostrophes are also used for contractions, where letters are missed out of words:
isn't (is not), doesn't (does not), we're (we are).
Bringing the two issues together is the often incorrect usage of 'it's' / 'its'.
Its is possessive, but does not require an apostrophe ('its shadow', for example).
It's is a contraction of 'it is'.