I'm British, but I can answer for the UK and US:

$100 — a hundred dollars or one hundred dollars?

"A hundred dollars" is how I'd say it in speech. "One hundred dollars" is how I'd write it on a cheque.

$201 — two hundred [and?] one dollar[s?]?

In the UK we'd say "two hundred and one dollars". In the US, they might say "two hundred one dollar[s]".

$1500 — fifteen hundred dollars or one thousand five hundred dollars?

"Fifteen hundred dollars" is how I'd say it in speech. The more "proper" way to say it, and the way I'd write it on a cheque is: "One thousand, five hundred dollars" (never "one thousand and five hundred dollars").

$1525 — fifteen twenty-five dollars or [one/a] thousand five hundred twenty-five dollars?

I'd never say "fifteen twenty-five dollars", I'd either say "Fifteen hundred and twenty five dollars", or "one thousand, five hundred and twenty five dollars". Americans might skip the "and".

For a non-English speaking country, say the number fully using "one", for the sake of clarity. In some countries though (such as the Netherlands and Norway), the use of "fifteen hundred" etc. is the same in that language too.

I am a native speaker with a careful ear. From my experience, I can tell you that when the millennium turned from 19xx to 20xx, we said "two thousand" plus the remainder throughout the aughts (01, 02, ..., 09). To use the "twenty" construction would have required acknowledging the zero digit: "twenty oh-eight, twenty-oh-nine" or "twenty-aught-seven" etc. Those were still heard a lot, however, as we were all new to the millennium and its numbering.

When it hit 2010, we started mostly saying "twenty-ten, twenty-eleven, twenty-twelve," etc., but it was not uncommon to hear "two thousand thirteen." This somewhat ambiguous pattern will likely continue throughout the teens.

You may be reasonably sure that once we hit the twenties, the "twenty-something" construction will overwhelm the "two thousand" one because "twenty" is still easier to say than "two thousand," and by that time it will also be more felicitous to use because "twenty twenty" has already made inroads into the general ear due to its appearance in popular culture as a standard of vision, etc.

Addendum

Just to add to an appreciation of the discomfort we feel with the awkwardness of "two thousand", consider the year 2000 itself. It's almost invariably referred to using the confection "the year 2000." Compare uses of "the year 2000" vs, say, uses of "the year 2012" in the Wikipedia articles on those years: "the year 2000" is referenced five times in the three-paragraph article (four in text, once in footnotes), while "the year 2012" in its article is given only once (all other times referring to that year simply as "2012").

Note that the millennial year was sometimes referred to as "Y2K"—although that term is blurred because Y2K could refer to the year itself or (more often, I think) to the turning of the millennium as a concept.

Now, given that we had primed our ears for "two thousand" by using "the year 2000," and that for thirty-odd years we had the example of the very popular Stanley Kubrick film 2001: A Space Odyssey, which everyone I ever heard talk about the film referred to as Two Thousand One and not Twenty-Oh-One, it seems reasonable to suppose that these uses laid a "two thousand" groove from which it was somewhat difficult to extricate our tongues.

Note that I am not saying it was impossible: people still did use "twenty-oh" while the rest of us muddled along doggedly using "two thousand" until 2010 (when, again, not all of us switched). All I am saying is that the millennium shook up the way we pronounce years, and we are slowly returning to the old pattern, the way ripples in a pond slowly die out after a rock has been tossed in.

Order will be restored. Be patient.

Addendum

Last night I was watching a news program and heard the announcer refer to events that happened in "two thousand nine and twenty ten" ... which was interesting.