I am developing new mobile app for swimming results
and I want to ask you: can I use your API to get swimming
results for the whole world (America, Europe, Asia and
Australia) or no?
You certainly can; you might have to extract them from some low-level data representation (such as raw page HTML or wikitext) though. Also if you publicly show the data you need to follow the requirements of the CC-BY-SA-3.0 license (to the extent it is protected by copyright or database law, which depends on the type of information and what jurisdiction you use it in, but usually it is easier to err on the safe side and just honor the license).