Mystère et boule de gomme

Timor is one of a surprising number of countries that use the US dollar as their currency. I've always found this idea fascinating, and puzzled over the idea quite a bit.

Where do they get their US dollars from? (They obviously don't print it, but they don't get bills by simply pulling paper money out of the US economy either: that would affect the US monetary system, actually causing disinflation)

How does the US feel about this?

Is it safe for (someone like you or me) to use a currency not guaranteed by the government of the country we are in?

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I did some homework on this, and it turns out that it's much less wild and crazy than I thought.

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First of all, the US actually encourages other countries to use its dollar. It helps supply their paper currency. This actually helps stabilise volatile emerging economies by fixing their interest rates and inflation to the (presumably) more stable and conservative US economy and monetary policy.*

*(although it's also criticised for contributing to the attitudes and sentiments that brought about the last economic crisis)

Having other people use their dollars is actually in the US's interest: it makes countries like Ecuador and Panama much more reliable trading partners.

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You don't have to read on:

If you haven't already figured out, I'm a pretty nerdy guy. Secretly, I read four or five different economics blogs. On one of them, I found an interesting bit of theory and speculation:

Gregory Mankiw, a high-profile and extremely influential US economics advisor (whose book on macroeconomics I used in college) famously wants to abolish the penny.

What does this spell for a country like El Salvador, which uses US currency, and which also has such a low price index that many common transactions happen in cents, and where people often need to break dollar bills to get change?

Could a country like that cope with adhering to US policy or would transaction volumes become impractical? What if they kept the penny legal tender and all the pennies from the US flowed there? How much would that be? (Billions?) (Is the size of their economy such that) it would cause catastrophic hyperinflation?

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I find currencies with "outrageous" units endearing, like Indonesian Rupiah, where it's about 10000 to the dollar, and 1 rupiah is meaningless. Ghana used to have a similar currency but they have since issued new currency with 1/10000 of the value.

I know, isn't it a shame?

Some charm remains: people in Ghana still talk in old currency even though they use new paper: they say "thousand" to mean ten cents" and "ten thousand" or sometimes "ten" to mean a dollar.