Goro/General Peppel is Itsuka's/Plamya's father and Tsubaki, his wife, died so that Goro could pursue World Conquest.
Episode 8 implies some strong relationship between them two and Kaori/White Falcon. Not only that, but it leaves some very clear hints that Goro and Tsubaki where married, and it's left pretty clear that Kaori and Tsubaki were sisters. Given how Kaori reacted when Itsuka came to Goro's aid and her comment that Itsuka "looked more and more like her", it's pretty likely that they're a family. Also, Itsuka said that Tsubaki died because Zvevzda and we saw in this episode that it was Tsubaki who made Pierre leave Goro's gang so that he could chase his dream of being a chef. Now, it's likely that Goro wouldn't leave his gang as long as his wife was alive so she had to die in order for him to leave and go chase his dream. Another hint to that is Yasu's flashback. In it we see that Goro was ready to die, most likely because he had just lost his wife, but changed his mind upon seeing Kate. He decides then to go on in honor of his late wife, dedicating his whole life to this dream. That would also shed some light in why Itsuka is so protective of Kate. Get all this information together and the result is that WMG.
Kate is the Physical Avatar of Lady Chou Chou from Mugen Souls and the entire series is really a Family Friendly, Saturday Morning tie in to Mugen Souls.
Okay. Think about it for a second. Kate and Chou Chou have the same powers. Right down to the complete adoration that results -with only people with high enough spirit levels capable of resisting her but still eventually serving her even if they aren't enslaved.
After the adventures of part 1, Ego-Chou Chou couldn't get enough attention so she decided she'll be human again in a different world. She comes to the world of Zvezda plot , lives as normal human for a few thousand years and finally decides that she can't contain her Ego and kicks off the events of the series.
Except it's now G-Rated and there's no mention of the sexual aspect of the powers she commands like Chou Chou wields.
Some stuff is rather bad for your health...
The governor of Tokyo, Asuta's neglectful father,
discovered that Kate was ageless and very old and also the other members of the inner circle of her "Zvezda" organisation had great powers and weapons to their disposal,
so he had the scientists do research about any kind of "unusual" things, that could give him an edge over his supernaturally enhanced enemies. One of the products of this research was discovering a way how to neutralize some of the weapons of Zvezda (an immobilizing agent for the KuruKurus, the magical rune array Natasha was shackled to or the gas to deactivate Roboko
). The scientists also discovered certain ways to increase the power of a normal person, but at a big price: It increased the weaknesses of the user's personality, so Governor Jimon, who was a little bit neglectful towards his family, but mostly OK and a little bit bossy, but not really bad, stopped giving a shit about family at all and became like a tyrant towards his subordinates and even his son. His wife had enough about him not giving a damn about her and him treating even her food as pure "gasoline" and not even realizing, that she, at the last evening of them together, made the food deliberately bad, so he would at least give her negative attention. He didn't, she had enough and left (he was never abusive towards his family, since he simply didn't have that trait for the empowering agent to increase). He then started to order his son around and wanted him to become the Vice Governor and eventual successor to his empire. The empowering agent gave him also the an immunity to the special gas (he used special cigars, that exhaled this gas). When he finally discovered, that his son not only told him to fuck off when he offered him a career in his regime, but actually joined his enemies, he had the White Light make an attempt to stage his death in a crossfire with Zvezda to have a martyr in his war against them. It didn't work out and eventually, Kate herself was forced to engage the Governor personally (he demonstrated his abilities of poison smoke resistance and Kate recognized the unholy rituals he used to enhance his power by a certain telltale signs, e.g. the red glowing eyes and a an dark aura and realized, that he not only wasn't quite human anymore like her, but also, that he became a monster)
Natasha defected from the Smoker's organization
Natasha was a member of the organization, that was behind the Smokers, that were in turn behind the governor of Tokyo
, just like her parents
. One day, she defected, though, her parents disappeared and the "fairies" went after her, but she was saved by Kate, who could drive off the "fairies" and take Natasha under her wing.