I would opt out for real time battles, along the lines of the system used in Secret of Mana. Also for a great English Translation of the game, that mixes translating with good dialogue. I'm playing through the CC Retranslation and it's a bit dry in parts for my liking, lol. Other than that, not much I can think of. They pretty much got it right the first time. I would like to see it, though, where when you level up, you get a certain amount of points to spend on your stats and skills; it would definitely make a more productive ground for pvp. Though, you'd have to add in more skills, too.
As for the thing with Lucca's mother, Lucca set up the gate herself so she could go back. I don't know how she did it, and the game doesn't really explain. Wish it did.
The thing with time travel and having consequences, think about it. This is the one thing they did get wrong when putting Chrono Trigger and Chrono Cross together, but if they did do it right, they wouldn't have a basis for a game. see, this is what I love about these games, the theological parts. People often have the mistaken idea that by going back in time you can change something to affect the future, but the fact is, with fate, you can not change the future because it would create a paradox. Your actions can only have out to one result. the key to this is, if you go back in time to change something, you were meant to change it and the future already reflects it, yielding no change whatsoever. You ended up fixing/changing nothing, yet you were still meant to be there in the first place.
Chrono Cross was the first instance I've seen of a non-fixed timeline. Meaning, you could go back and change something and have it have an effect on the future. Oddly enough, there can be no fate in this, no destiny, because whatever you do can be undone. It's wildly out of control and would never work in reality, because there would be an infinite amount of dimensions to reflect every minor difference. Every time you changed something, even with the passing of human foot in the dinosaur period, where no human should be, it would have a huge chain of repercussions. Much like the saying: A butterfly flaps it's wings on one side of the world and it creates wind on the other side. But how does the Butterfly know when to flap? It doesn't it just flaps. Chrono Cross did a great job of making it believable, but when it comes down to terms of reality, it just isn't possible, that we know of. Back in the 1400's we knew the earth was flat, though, if you get my point.