FATE would never even be interested in controlling Crono or effecting any changes on the mainland, as FATE's sole mission is to maintain the El Nido paradise and prevent mainland interference to preserve the future as it was in Chronopolis's own history. Lynx did not even exist until 1010 A.D., five years after Guardia fell. Later, Lynx did manipulate Porre and the Acacia Dragoons as an agent of FATE towards this end. As for Magus, he is Magil in the Radical Dreamers continuity (replaced by Chrono Cross), and found Kid in the modern era to watch over her until she was ready to learn her true heritage (Schala, unaged to a baby and sent to the modern era after the Ocean Palace incident). Remember that the RD continuity is no longer canonical.
Masato Kato purposely left the Fall of Guardia and other details a mystery, as he lobbied to make Chrono Break in 2001 before leaving Square entirely. He's back with the company now, but apparently Square won't throw him a bone. He's probably working in hopes of getting a chance at a new game.
Anyway, most of those questions aren't able to be answered outright, but there's a lot of evidence pointing to outcomes and causes. Not to spam, but it's all centralized here:
Chrono Compendium
Chrono Compendium