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Is DA work pretty much a prerequisite for any sort of criminal law? Do small criminal law firms hire fresh law students, do they have summer internships?

Sadly there just isn't as much money in criminal defense firms as other areas (except white-collar defense, of course). So they generally don't have structured summer associate programs, at least in my experience. But that isn't to say it isn't worth applying. A lot of great summer jobs can be had outside of OCI/ summer associate programs. At least on the criminal side of things, you have:

1. DA internships
2. DOJ SLIP
3. Attorney General's Office Criminal Division internships
4. State/Local/Federal Public Defender Internships
5. Internships with criminal defense firms obtained outside of OCI.
6. Prosecution and Defense Aid Clinics.

I'm not certain, but I think the Criminal Division doesn't participate in SLIP.

As to DOJ, that's true, but other divisions have sections that do exclusively criminal work. Antitrust (field offices and nat'l crim enforcement section) does white collar crime prosecution like bribery, kickbacks, tax evasion, etc. Tax, Environmental, National Security and Civil Rights also have sections that do exclusively criminal enforcement in their respective areas.