DOGE is not necessarily about fraud. Their summary of cancelled projects for USAID for example is often vague. For example, "$14M for "social cohesion" in Mali." As a reader, I have no context for this program, its impact, or who ran it. I don't even have the ability to discern whether other things were lumped in. Can I guess this was aimed at preventing further in-roads of Al Qaeda? Who knows.
An actual cherry-picked example of DOGE's potential fraud finding is at the SSA where Musk showed his query of "DEAD" = "FALSE" (I am paraphrasing a bit) yielded a huge number of folks over ages 115. Context is what is scarce. Are they receiving payments, are there other reasons for why the query returned those results, what other context do I have to interpret these results? Again, I have no idea.
I think the safest way of couching what is going on, is a drastic curtailment of government programs and employees. Equivalents to this? Maybe Gorbachev. I am sure there are other historical parallels, but they are probably apples to peaches comparisons at a certain level.
And to your last question, I am not sure if anyone really knows the problem/s that are being addressed right now other than debt and the capability to pass a tax cut.
I am surprised people are comparing what Trump and Musk are doing now to Putin when in reality it's closer to Gorbachev (as you mentioned) and what the Chicago school did under Yeltsin. For those not aware, they cut government programs, reduced regulation, and privatized many government entities. The result was a catastrophic reduction in GDP and people's wealth. If what is about to come something as devastating, I really hope not. A recent example is what Milei is doing and he had similar results, resulting in a large increase of poverty.