As I mentioned before, it takes place in the same world, in a very, very small area. Ever notice how you cant leave the El Nido area? The area outside of that is the world we knew in CT. They mentioned Guardia a few times, but they never said what happened to Crono, Marle, and Lucca. I assume they'd be dead, seeing as Guardia was overthrown, and I doubt they've have just sat there and let it happened.

Lavos is not in a dragon form, the Lavos of Cross is part of the original Lavos, a Lavos spawn, basically.