There are other gene editing systems out there, such as zinc finger nucleases (ZFNs) and transcription activator-like effector nucleases (TALENS.) ZFNs are nucleases fused to a zinc finger DNA binding domain. You can engineer ZFNs to target a specific nucleic acid, just as CRISPR-Cas9 does. However, CRISPR-Cas9 systems are revered for their simplicity, essentially just needing the DNA sequence you want to target. TALENs functions like ZFNs, a nuclease bound to a TAL (transcription activator-like effector), which recognizes a specific DNA site. There are other gene editing tools, you can see that among Cas9, ZFNs, and TALENs, the structure/function of the tool is conserved.

Cancer cells and cells infected with HIV have shown to respond promisingly to CRISPR-Cas9 treatment. Ironically, CRISPR systems originated in prokaryotic species, as a defense against mobile genetic elements (MGEs), like viruses or bacteriophages. But CRISPR-Cas9 is being studied as a defense against viral infections, targeting the viral nucleic acids at different stages.

Proteasomes are complexes that degrade proteins rather than nucleic acids. For cleavage of nucleic acids, you’d want to look at endonuclease or exonucleases, restriction enzymes. Proteasomes typically are involved in degrading misfolded proteins (look into prions!), or proteins that are no longer needed in the cell. Just a minor correction, hope it helped. :3

Basically what Marie said. You usually need enzymes to cut and edit DNA. You can cut some out to stop a function of a piece of DNA or even add some in. ZFNs, TALENs are slightly 'older' technologies and CRISPR is the new technology, which is being used for the purposes above. It may be enhanced/improved in the coming years and I wouldn't be surprised if there weren't other DNA editing technologies that appear in the future too.

Bear in mind plenty of viruses do not have any DNA, using RNA instead. But there are other Cas proteins that cut RNA, so you can still apply that kind of approach.

It's not necessarily going to be all that effective for typical viral infections, as it's hard to deliver a lot of CRISPR-Cas machinery in vivo, whereas a viral infection can create huge numbers of viruses.

Where it could be exciting is in potentially permanently curing HIV infection. You use other drugs to knock the infection down, but some of the viruses have integrated into the DNA of host cells, where drugs do no good. But CRISPR-Cas9 could come along and destroy those viral DNA sequences.