You are talking about
the word mess.
Where a mass lives
and which the mass dislikes.
According to OP, people live in messes. People as a whole, however, tend to dislike messes (the sort that are unclean).
When one of the arms eats with a friend.
According to a Google search, mess (as a verb) can mean to "take one's meals in a particular place or with a particular person, especially in an armed forces' mess."
If you do it up, you ruin.
If you mess up, you might have ruined something.
I've warned you already, don't do it with me!
Refers to the phrase don't mess with me!
While in a it, you’re entangled in trouble
The phrase in a mess can refer to being in a situation full of problems/trouble.
A icky mash, also a gooey muck.
I had to check this one online, but apparently "mess" is another term for "gooey muck".
And the hint
Mum certainly doesn't like it, when you make a ____.
refers to the fact that:
Mothers often don't like when their children make messes. (This also ties in with the puzzle's title.)