I suppose you could break this down into a few sub-questions:

1. How did people pay for goods and services between the founding of the First bank and the closing of the Second? Did they exclusively use the US Dollar, printed by the central bank? My understanding is people used the US dollar predominantly, but were free to use other forms.

2. How were taxes collected? Could they only be paid in the Dollar? My understanding is that was the case.

3. If the dollar was the sole, or at least main, species of currency, then what happened when the Bank shut down? Did the dollar disappear? What did people pay for goods and services with, and what did the government accept as tax payment?

This third point is the crux of my question.

I understand that when the Second Bank was not re-chartered, smaller banks were formed and "treasury funds" were funneled to these, from the Second Bank (although I'm not clear what the "treasury funds" were either - if the US dollar was defunct, then it must've been gold/silver that was transferred from the central bank to these local ones, right? And how the hell do you decide who gets how much?). My understanding is each State formed its own Bank, and private banks also cropped up, each issuing their own currency. But what the bloody hell happened to the US dollar then?! If I had $1m USD, what happened when the 2nd Bank closed? Was I issued their gold amount in return or what?