I'm sure this was in no way a final draft, and you probably don't need the critique, but I just thought I'd point out a few things that stood out in odd ways for me (good or otherwise):
{Gina}: {Crono}, sleepy head, let's get up now!{full break}
I might just go with something like "Up and at 'em, sleepy head!"
{Gina}: Oh, finally! I swear, {Crono}, you'll be{line break}
the death of me one day...{page break}
That's kind of creepy... are you planning on killing her off?
{Girl}: Oh no! Don't tell me I lost it! Daddy'll kill me!{full break}
Daddy sounds a little more snobby than Dad, coming from Marle. I feel like she usually just calls him dad. I could be forgetting her using daddy in her lines, though.
{Marle}: {Crono}? Neat name! Nice to meet you, {Crono}! Now lead on!{full break}
Haha, I like that you used the word neat. It's so appropriate.
{Old Man}: Sorry, son, I don't have time to talk.{line break}
FATHER??? OMG SPOILERZZZZ
{Marle}: Hehehe...you're such a pig, aren't ya {Crono}?{full break}
Maybe make it more of an observation than a question. "Hehehe... you're such a pig, Chrono..."
{Little Girl}: Miss Buttons! Oh, thank you so much for{line break}
bringing my cat back!{full break}
Miss Buttons is the best name for a cat ever. Good job.
{Young Woman}: I heard {Lucca} and her dad've made another{line break}
one of their inventions.{page break}
Dad've?
(If walk away once){Marle}: Give me just a second, okay?
(If walk away twice/all consecutive times){Marle}: Jeez, {Crono}! There's no
need to drag me by the arm like some kidnapper!{full break}
This is hilarious. It got me thinking... it would be kind of interesting if based on your actions here, Marle actually did get a certain “impression of you” during the fair, and it determined her actions for the rest of this chapter, until she disappears (kind of a prelude to how the trial would turn out). If you've been a “real jerk” then during the time warp scene maybe she would act all distant to you while you're checking out Lucca's invention. Could make for some funny dialogue, and it would probably flesh out Marle's character a little more. I can just picture going through the time warp scene with Marle acting all sulky. And of course after Chrono rescues her, it would be such a nice thing for him to do to take on the task of time traveling to save her, she would forgive him completely in the moment, which would explain why she would still get upset when your trial is rigged. What do you think?
{delay 12}{Marle}: Hiya. I'd like some of this stuff, please.{full break}
{Candy Seller}: Here ya go, young lady.{full break}
Add in the "tastes like chicken, but better" here too
{Marle}: It looks like a lotta fun, {Crono}! I'll watcha while{line break}
you try it out.{full break}
Watcha? How long has this girl been out of the castle?
{Taban}: Don't worry, {Crono}, we tried it out on our pets!{line break}
So there's no reason why it shouldn't work on you!{full break}
HAHA! Amazing. You can probably drop the 'so' at the beginning of the second sentence.
*Marle ends up in the Gate*
It would be sweet here if she called Chrono's name for help. I think it would be cute...
One last thing, while I was reading through I started realizing that people say Chrono's name... a LOT. For example:
{Lucca}: {Crono}!{full break}
{Taban}: You're actually going after her, {Crono}?{full break}
{Lucca}: Okay, listen up, {Crono}. I don't know where this{line break}
machine is gonna send you, but it looks like we've got no choice.{full break}
I know that in the original this was still the case, but it might be something to think about. in a lot of these lines, we'll know the character is talking to Chrono (the first scene with his mother, for instance). If you took out a few occurrences of his name, it might just sound more natural, without necessarily confusing anyone. Know what I mean?
Besides the things I mentioned, I absolutely love this (and some of the things I meantioned were positive anyway). You did a nice job of making people sound more natural, and you didn't change anything so wildly that anyone should give you crap. I look forward to seeing more... And I'm sure you don't need it whatsoever, but I enjoy proofreading a LOT, so if you did want a proofreader, you know where to find me. Great job!