1-Why did Marle Disappear when Lucca first arrived at the Middle Ages?
I used to think it either had something to do with Frog somehow no longer being able to save the queen in time (but couldn't figure out why) or, as Thought said, something to do with Lucca's presence in 600AD. But I just started a new game now and I think it might actually be Marle's fault to begin with - hear me out.
When Crono comes to the castle, you have the option of talking to the Chancellor, he then goes up stairs and ponders the Queen's escape and then
returns to the cathedral.Perhaps Marle's appearance drastically changed the time that the Yakra had planned to return to the cathedral to kill the Queen. Remember that when we first see Frog, he jumps down from the rafters to save Lucca. Who knows how long he had been staking that place out, or how long he would have continued to do so before entering. Crono and Lucca barging in probably helped to speed up that process, allowing the Queen to be saved in time. Also remember that Crono and Lucca never even considered saving the real Queen until Marle vanished, so the latter had to happen for the former to occur. Finally, we know time is really really tight because Crono and Co. walk in on Yakra just as he is about to kill her. Obviously having 3 people taking on enemies would help you move much faster than 1.
Guards find Marle > Yakra returns to cathedral early > Crono and Lucca decide to find real queen > They help Frog infiltrate > They save the queen just in time
That is my current opinion, =)
Edit: Even stranger is that Lucca says : "Something must happen to the Queen in this era if she isn't rescued. And if something happens to her,her descendant, Princess Nadia, will never come into being."
Right before that she says "There might still be time..."
So, looking at the way Lucca is speaking, its as if the doubt surrounding the Queen's survival makes Marle vanish, but not erased just yet from history. Hmm it is strange how that works...