Eh, I honestly doubt that a) Janus is dead (since like Zaper said, Lucca alluded to his presence in her letter) and b) even if he were alive, he'd be watching that closely over Kid. It's cruel, but true — Kid is only a clone. I believe Janus would much rather search for the real McCoy than resign himself to the fact that Kid is probably the closest he'll ever come to meeting his sister again. Hopefully if/when the next game in the Chrono series comes out, it'll fill in quite possibly the most annoying hanging plot irresolution in the history of RPGs. Besides, if one watches the Final Fantasy Chronicles FMV, Kid is found with Schala's pendant already on her person — I seriously doubt that Janus would just give his infant niece-clone the pendant and than leave her in the wilderness to fend for herself until Lucca stumbles onto her. The pendant is most likely a gift from Schala to her daughter-clone, to protect the child as it protected the mother.
AND Squeenix killed the whole Guile = Janus-watching-out-for-big-sister's-daughter-clone plot thread anyway — who knows what they have in store for Janus and Schala now? I doubt they'd continue on with Janus watching over Kid now that Schala's been freed from the Time Devourer and the two have been reunited, unless they'd like to remake Chrono Cross (hey, I'm not complaining).
Other nitpicky things:
- The Radical Dreamers are, in fact, operating in Home World as well — the guy completely off his rocker taking English tea in this appropriately-rated Teen game in Orcha's restaurant mentions them as working on the mainland, basically repeating his Another counterpart's exact words.
- Lucca is, more than likely, dead in both worlds. If I remember correctly, the Lynx in both worlds attacked the orphanage and kidnapped Lucca, although I doubt they had the same motivation, considering Another's Lynx was after the disabling of the Prometheus Lock and Home's Lynx didn't even have a Chronopolis to muck around in. And besides, even if others feel they're more abberations than anything else, I still believe the children at the Liberty bell Nadia's Bell and the DBT's Angelus Errare are the ghosts of the Chrono Team, reverted to childhood because, I don't know, they're inordinantly cute or something.
- On the same tangent, Crono and Marle are also most likely dead — I hate to say it, but it's wishful thinking that they survived the Porrean attack on Guardia. I keep thinking of the Bolshevik Revolution in 1917 Russia and how the royal family was eventually killed, to ensure that no resistance movements sympathetic to their cause rise up and try to retake the country.
- Finally, that damn moon question again! — I'm 99% positive that when the Time Crash pulled Chronopolis back to whatever arbitrary date has been settled on lately (7600BC or what have you), Dinopolis was pulled back as well to counterbalance the humans' construct along with its red moon, representing the power of the Reptites and their Dragonian descendants or some such nonsense. The white, yellow, cream-cheesy moon is the moon that has always existed throughout the timelines we've witnessed in the Chrono series; the red moon is the Reptite moon, reflecting a time when Lavos hadn't stuck his big nose into everybody's business. It's all symbolism, Red Moon v. White Moon, Dragonians and Nature v. Man and Technology.