I'm gonna explain some stuff I learned from being a hardcore Guilty Gear fan.
The connection between Sol, Dizzy, and Justice.
If you listen to the Drama CDs you learn that Dizzy's mother is Justice. (yes newbs, Justice is a female) Dizzy is of course half human half gear, which means her father had to be a human. One theory draws out the fact that Sol might actually be her father, sence Sol is doing alot to keep her safe. He probably got some of his DNA used in the creation of the Justice gear over 100 years ago, but that's probably not what happened. Playing Dizzy's storymode in X2 she is being attacked by I-No and then in a flash Sol comes and rescues her and brings her back to reality. As Dizzy recovers she has a feeling that she was just near her father just now.
The connection between Faust and Axl to Zappa
Zappa was your average joe who's body go possesed by a female spirit who hates men. That spirit may just be connected to either Axl Low or Faust. When Axl started his time travel running about he left behind a girl in his own time back in the 20th century named Megumi. It is beleived that the spirit that posesses Zappa is Megumi's dead sprit, wroght with sadness of having Axl, the one she loved leave fo years and years.... or maybe. Back in the Guilty Gear era, Faust was a great doctor who can cure many ailments. He was operating on a young woman, she died while she was under Faust's knife, so he went mad from that, changed his name to Dr. Baldhead and went on a mass murder rampage. But then he learns that the girl's death wasn't his fault, so he then went back to being a healer and called himself 'Faust', covering his head with a paper bag becuase of his guilt to nt show his face anymore. The spirit posessing Zappa may as well be THAT girl. Those are the only theories I know about that.
Theory of Axl and Raven
Raven is shown as a servant of "That Man". If you play Axl's storymode you're given a pretty big clue that Raven is actually Axl from the future. After Axl fights and defeats I-No he's confronted by That Man and Raven. Axl's body begins to slip into another time or place as Raven speaks with him. Raven mentions that when two objects of exact same identiy from different times approach one begins to slip away. So in other words, Axl becomes Raven at some point.
Discuss other theories. And no bashing the story because it's fighting game, please.