In unoccupied Medina, Melchior's adopted grandson dreams of avenging the parents he never knew, unaware of the royal blood that flows through his veins...
In the El Nido archipelago, an intrepid youth dreams of an adventure the world has forgotten and a girl who is unforgettable, not knowing that his quest to find her will take him to times and places beyond imagination...
In military-controlled Porre, a mighty general dreams of immortality and world domination, there being few left who can oppose his schemes...
In the sea of time, a beautiful princess dreams of returning to the one she loves, but she has lost her way...
And beyond the walls of time and space, an ancient king dreams of becoming the lord of time itself, his far-reaching plans already in motion...
The planet's dream has become a nightmare, and when the three triggers act as one to cross the final gate and enter the realm of Zurvan there will be no averting the...Chrono Break!Heh, anyway, moving away from fan musings to the questions you posed...
1. Would we see characters from the other games? Would the setting stay the same, or would the story take place elsewhere?
Hm...personally, there are two major approaches I think of when considering what a third game in the Chrono series might be like. It could follow the Chrono Cross model, starting in the same world in the "present" but featuring new locations and starring a new cast of characters. The story would be related to the previous installments and feature references to and cameos from both, answering some questions, raising new questions, but capable of standing on its own. Or it could try to be a "culmination" of the series, continuing the stories of both Trigger and Cross, providing closure to both casts, and definitively resolving this time traveling epic.
Both options have advantages and disadvantages, and both would require a really good story to even begin to meet expectations. I might prefer the latter for the sake of closure, but on the other hand the unanswered questions and uncertainties are part of the charm of the two games, in my opinion, and I like how, instead of spelling everything out, the games give us the freedom to fill in the unknown with our imaginations.
2. Time travel, dimensional travel, or (oh god) both?
Either, both, or something different would be fine with me so long as it is interesting and enjoyable. Besides, the two aren't mutually exclusive, and perhaps part of the game could feature time travel before some momentous event occurs (collapse of a timeline?) and a jump to dimensional travel takes place. Including dimensional travel could also open up the reptite/dragonian dimension in a new game, and that could be very intriguing.
3. Akira Toriyama or Nobuteru Yuuki? Or some new blood?
Tough question. I prefer Yuuki's art style in Chrono Cross over Toriyama's designs in Chrono Trigger, but I think creating a game that looks great and will continue to be attractive as graphics and modeling improve is more important than who the lead artist is. Chrono Trigger is still visually appealing (at least on the small DS screen) despite being released so many years ago, and Chrono Cross is a delicious feast of beautiful color for the eyes. If a new Chrono game is made, it might be better if they went with something enduringly memorable like Valkyria Chronicles' cell shading rather than attempt hyper-realism.
4. A huge team of playable characters like CC, or a smaller team like CT?
I might be in the minority here, but I rather liked Chrono Cross' extensive cast. The Cross cast had diverse personalities and motivations, and I found them to be a refreshing change of pace from the common "three to seven characters drawn together by fate and coincidence who you'll know just about everything about by the end of the game" pattern. Still, I will admit that some of them were somewhat...silly, so maybe a compromise between Chrono Trigger's seven and Chrono Cross's 40+ would be advisable. Or, perhaps even better, have a smaller group of "core" characters with a huge cast of NPCs that join and leave your party as playable characters as the story progresses, with some characters exclusive to certain divergent paths players choose like in Chrono Cross for additional replay value.
5. Battle transition for encounters (CC), or fight right on the field (CT)?
Either one's fine with me so long as it doesn't take too long for fights to start and looks good.
6. A battle system like the other titles, or entirely different?
I played the games more because I enjoyed the story than because I enjoyed the gameplay, so as long as the battle system continues the tradition of techs and offers at least a reasonable challenge without being frustratingly convoluted there's a good chance that it'll be pleasing to me.
7. Console or portable?
Console. While both the DS and PSP are powerful systems in their own right, I view the Chrono series as a console series and would like to see what a possible third installment could accomplish by utilizing the technological potential of the next generation systems.
8. Is it possible that both CT fans and CC fans alike can be pleased?
Depends on what you mean by your question. If you're asking whether everyone would be pleased with a third game, that is unlikely. It can be very difficult to please everybody, especially with a series as beloved and with as many beloved characters as the Chrono games, and trying to do so could weaken the final product. However, I imagine that many Chrono Trigger and Chrono Cross fans would be pleased with a third installment if the game is good, even if there are segments of the fan community who feel differently.
9. Is there hope for another game in the first place?
Yes. Both games were financial successes and critically acclaimed, and the series has clearly not been forgotten. With the release of Chrono Trigger DS there are even more reasons to encourage hope in the possibility of a new installment. None of this means that there will be another game, of course, but optimism is not uncalled for here.