It is the set of all elements we are considering or dealing with in a given problem. We use a capital U or sometimes capital E to mean the universal set.
Now take ANY two sets, A and B. If every single element of set A is contained in set B, we say A is a subset of B.
The empty set is a subset of every set.
Every set in contained in the universal set, so they are all subset of it.
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The null set. It is a subset of every set.
Yes.
If I understand the question correctly then a is a proper subset of u.
There are 250 subsets. That is 1,125,899,906,842,624 of them and I am NOT proposing to list them.
The null set. Every set is a subset of itself and so the null set is a subset of the null set.