If they are, can anyone change the wording of the exercises and use them? Also could that person be in another country and translate the exercises to another language?
You would not be permitted to do that.
Copyright protection extends to:
- Works of authorship,
- That are original, and
- That are fixed in a tangible medium.
Olympiad problems and standardized exams meet all these criteria and are therefore generally going to be protected by copyright, giving the author the exclusive right to make copies and to make derivatives works of authorship. Making derivatives includes changing the wording of the problems, and it includes making a translation into another language.
So anyone who did what you are describing would therefore be infringing the author's copyright.
It depends on the nature of the questions. To the extent that the question presents a set of facts with a brief statement like "Account for these data", (a) that stub is not sufficiently creative that it is protected by copyright and (b) it is easy to express the same idea with different words, e.g. "Analyze these facts". Facts are not protected by copyright, though a clever ordering of the facts could be.
Copying unmodified is copyright infringement. Changing the wording means you create a derived work, so it's still copyright infringement.
What you can do is write your own problems, exercises and so on, using what you remember about the original problems. To be safe, you would create some evidence that you have written the problem yourself (even though heavily inspired by someone else's).