Translation:One thousand dollars and one thousand hryvnias
No, тисяча is just one thousand. Thousands of dollars/hryvnias would be тисячі доларів/гривень.
It is "одна тисяча," but "одна" can be omitted in this case (both variants are accepted).
I'm trying to match sound files - I'm pronouncing 'тисяча' correctly in the first half of the sentence, but I'm somehow mispronouncing it in the second half? I know that i may actually be doing it - but I've got to be legibility close: I clearly have the ability to get it!