"Please say it one more time."
They could improve the help text by either making "more" show "再" in this particular case, or by treating it as a whole phrase. This is the way German handles some of these things, and in my opinion it is one of the reasons why that course is so much easier to work through (and more useful) than the courses which don't have as many phrase-level translations in the hover-over hints.
The hints in this Chinese course are quite often the most confusing part of a task, which is not making learning any easier.
There are over one billion people who speak Chinese, and China is a relatively large, culturally diverse country. Just because you have not heard something, that lack of personal experience does not automatically make some alternative "more common," and something being "less common" in your experience does not make it incorrect or even "less correct." Whether you have ever heard it before or not, 请再说一次 does indeed mean "Please, say (it) one more time." Maybe I have never heard anyone say 请再说一遍 before, but my lack of experience with your preferred alternative has nothing to do with whether it's correct; in fact, 请再说一遍 makes sense to me, too, but 请再说一次 is (also) perfectly good Mandarin.
In my choices 再说 were put together as one word (one tile). Should i guess that when combined, 再 and 说 mean "repeat" and that the order of the two characters is not interchangeable?
In a previous question, i structured this sentence like this: 请说再一次 (reversing the characters "say" and "again") but it was marked wrong.
请(main verb at the beginning, because you do not need a subject here) 再(adverb in front of the verb it defines) 说(2nd verb) 一次(how often sth is done comes always after the verb it defines [走一趟、看一遍、跑一回])