Which hash function to be used with DSA 2048
This is reasonable and gets at most of it.

One critical limit of DSA with a 160-bit prime group is that you can't get better than 80-bit collision resistance by the birthday bound.  You really want a uniform random function from whatever is your finite message space to $\mathbb Z/q\mathbb Z$, but that's a pain to achieve, so you might choose a $\lceil\lg q\rceil$-bit hash function like SHA-1—but SHA-1 is known not to be collision-resistant at the maximum possible 80-bit security level in the circumstances.

You might be concerned about the small modulo bias of reducing a uniform random integer in $\mathbb Z/\lceil\lg q\rceil\mathbb Z$ modulo $q$.  You might be concerned about security against multi-target attacks.  If you are concerned about that, then you might choose a double- or 1.6-size hash like SHA-256 or BLAKE2s, and attain collision resistance up to the maximum possible 80-bit security level.

For a loose comparison, a double-size hash, SHA-512, was chosen for Ed25519's ~256-bit group, for several conservative reasons.  Now, the comparison is not precise, because Ed25519 is a qualitatively different signature scheme—and superior in pretty much every respect, except compliance with US government standards, to DSA: it uses the hash in a different way so it doesn't even rely on collision resistance, it doesn't break catastrophically and barf out your private key if you use it on a machine with a broken RNG, it's faster and smaller, etc.