Computer spends gold ???

It doesn't spend gold, and in fact can't.

Well I look at it like this, the game gave a country I was attacking a city ( I think that suxs too) and in a little over a hour it had a anti tank gun in it. I know the only way I can build a gun that fast is to spend gold on it. So either it the same as using gold or the game is set to build what ever it wants whenever it wants......

Or maybe the city was already producing an AT gun. I tell you, AI doesn't spend gold.

One thing I notice AI doing: they seem to have a focus on just one unit.

For instance, I've seen countries have level 6 destroyers as early as possible. And with absolutely nothing else above level 1. Or a country have a level 5 submarine, and no cruisers.

AI tend to spam more defensive units-infantry, militia, AT, AA, subs, destroyers. They'll often use everything on those units alone. So they don't use gold. They're just using all of their resources for defense only. Which makes sense.

Guess it is what it is, so I will adapt and overcome

As Pablo stated, when a province is captured or revolts, it's production continues given the buildings to produce that unit still exist. If the building is destroyed or damaged, the production is stalled until the building is repaired or rebuilt. This works for both players and AI.