Is it possibile to have a mermaids' city split into three small pieces all just one river hex far each another?
No. The Mermaids' ability only lets you use one river hex to connect a city together. From the rules:
You may skip one River space when founding a Town. (You decide if and when you want to use this ability. When founding a Town in this fashion, put the Town tile on the skipped River space. Of course, you may build Bridges as usual.)
The reminder text also supports this fact since it emphasizes that you place the "Town tile on the skipped River space" which would be ambiguous if you were not limited to using only one river hex. Without this clarification, it would be hard to determine where one directly-adjacent city ends and the next begins on the river.