If I select Feral Ningyo with it, can I then during a water conflict use the Ningyo's reaction to put it into play or would I have to pay fate cost of Ningyo?

If you select Feral Ningyo, you can play it (by paying its cost) but you cannot trigger its ability to put it into play, as it is not in your hand. The lasting effect of the event only allows you to play the card from its removed-from-game state, at which point it will enter play as normal.

[Tyler Parrott, 5 October 2018]