Will they make a second Chrono Trigger?

Answer 1

After Chrono Trigger (SuperNES, Nintendo DS), came Chrono Cross (Play Station), which is in many aspects, a continuation of the Chrono Trigger story, told through the lens of a new character, Serge. The plot starts as a near re-creation of a Japanese choose-your-own-adventure type game, Radical Dreamers. In Chrono Cross, Lavos is gone, but in his place is FATE, and the Time Devourer. Serge doesn't time travel, but rather crosses through two parallel dimensions. The music, like that of Chrono Trigger, is incredible. It's definitely worth a run if you can find a copy and the platform with which to play it.

As for further games, nothing is official, and fans have been hoping and begging for years. However, Square Enix's insistence on vanquishing all attempts at fan-made games give many hope that plans to make a third game might be in the works at some point.