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There actually isn’t such a thing as a “natural rate of unemployment”

I never claimed there was, I only claimed that 4% is right around ideal.

It seems somewhere between 3-6% is a good range. If you drop too low, you get inflation due to wage inflation (workers demand more pay) outpacing regular inflation (more money chasing the same number of goods -> inflation). If you go too high, you get do deflation due to reduced demand.

That's why monetary policy tends to town tighten with lower unemployment (cool off the labor market), and it tends to loosen with higher unemployment (encourage investment and therefore job creation).

That said, this is a simplistic view of monetary policy, and employment is merely one of many factors central banks look at.

The governments has to spend before it can tax, or else there wouldn’t be any money to tax.

That's only true if you lump monetary policy with "government spending." In the US, the Federal Reserve is largely separate from the rest of government, so it makes little sense to combine them in your simplistic explanation.

The ideal scenario is that government spending matches receipts, meaning there's a plan to pay for all spending. If there's a deficit, monetary policy needs to step in to issue debt to fund the gap, and that's inflationary. If there's a surplus, monetary policy needs to step in to buy back debt, which is deflationary.

They're absolutely related, but the perspective you seem to be talking from tends to justify deficit spending: "we can always just expand the money supply." That works until it doesn't, such as with Venezuela, Argentina, and Turkey. That's a large part of why the Federal Reserve is independent, and why giving the legislative wing (or worse, executive wing) of government direct control over monetary policy is so dangerous.