Could be American dollars, Canadian dollars, Australian dollars. In fact, per Wikipedia, there are 37 economies that use dollars. https://en.wikipedia.org/wiki/Dollar#Economies_that_use_a_dollar
Exactly. The USA didn't even invent the name "dollar": the word comes from the name of a silver mining town in Bohemia called Joachimsthal. The coins made there were know in German as joachimsthalers, which was shortened to thalers. This was then adapted into Dutch as dalers, which was the name they gave to their coinage in use in New Amsterdam. In time New Amsterdam became New York, but the new English-speaking colonists carried on calling their money by the same name, albeit respelled as "dollars".
Because we don't use that verb in continuous tenses that way in English.
"cost" is not an action that the shirt is doing; it's more of an attribute that is always true.
So we use the present simple tense: "that shirt costs twenty dollars".
(This may be connected to the use of present simple for repeated and habitual situations, e.g. "I visit my father every Saturday" or "It rains here all the time".)