You guys are just emoting onto Serge...He's just an emotionless husk that the player can pour their own perceptions & feelings into. That's a "plus" of having a silent protagonist, I guess...Also, Serge, like Crono, talks when he has to make plot choices...and he also gives his name to Kid (as Crono gave his to Marle). But I think it's stretching things a bit far to say that Serge loves Kid...or anyone for that matter.
I don't see why Schala would look for Serge. Sure, his cries as a child are what ultimately allowed her to be saved & he also came to her rescue (thanks in part also to Belthasar, of course) by using the Chrono Cross...but aside from that, what reason would she have? Not only that, but, wouldn't she, having sent him back to where he came from at the end KNOW where he is? I mean, why is she in Tokyo?
Kid, I think, isn't looking for Serge either. I think she knows he'll just stay w/Leena...I think Kid's out to find herself. After a large part of her life revolving around just survival & revenge, she's got to find out who Kid really is and what the world has in store for her.
No matter whether or not there was a Schala/Kid merge, I think Magus will find them or vice-a-versa.
Also, who WOULDN'T cry after Kid's speech as a kid after Serge rescues her from the burning orphanage??? That was some sad shit she was laying down, man. Even I was tearing up.