Everyone is convinced that Fatora is really Rune's sister. As Fatora doesn't have parents and that Rune isn't authoritarian, she became a Jerkass Spoiled Brat. When OVA Makoto comes in El Hazard, Rune know who he is and acts. Finally, if Fatora listened Makato and didn't punish Ura, this is because she had the feeling that she must obey.
- Actually, his power was stated to be the ability to communicate with the Bugrom. And Jinnai was already more of a genius back on Earth than most people give him credit for. Keep in mind that he had the second highest test scores behind Makoto.
- To add to that, even on Earth, Jinnai obviously had a knack for rules lawyering and finding the most simple and effective ways to solve his problems. Luring Makoto somewhere using one of Nanami's love letters and then going after him to tie him up and secure his position on Student Council may seem like something that just about anyone could come up with, but that's the beauty of it. A plan doesn't have to be complex; it just has to work, and he's always been smart enough to know that. He'd have even succeeded, had there not been supernatural intervention at the last second. The guy is a Bunny-Ears Lawyer, not a moron. The only reason he never took over Earth was probably lack of an army. Once he got the Bugrom, he was golden.
When looking at Makoto, Fujisawa-sensei, Jinnai, and Nanami, they at first speak about going home to Earth but then quickly give up on the idea. It's because they understand that they can't go home, at least not at their present time. By Makoto becoming a Time Lord and wielding the power key staff as his Tardis, he not only is able to reunite with his true love, but his friends—should they choose to—can finally return home as they like. It would also give the ability of the people of El Hazard to travel to Earth as well, as the still images of the credits of the first OVA should give us.
So in this sense, as a Time Lord Makoto has become a human Eye of God, but he can control it more freely via the power key staff.
It would explain a lot of their motivations. Makoto is The Ace at his school and is good at most everything he does. Jinnai tries to be as good, but fails miserably. And Nanami gives everything she has as a reporter for the school newspaper. Being an overachiever is common amongst Japanese students, but in the case of the trio they may be overachievers to prove themselves to everybody around them. They don't want people looking down on them for not having families, and so they try their best to stand out and make impressions on people that will allow them to think of them as anything else but poor orphans.
This is why Jinnai has such an inferiority complex and why he strives to defeat Makoto. He doesn't like the reminders that he is nothing and so he tries to be better than he is. When he can't do so because Makoto is better than him, he resorts to cutthroat tactics to be the best. He sees a kindred spirit in Makoto in that Makoto has no family, but it repulses Jinnai to see someone with less than himself (as Jinnai at least has his sister Nanami) do much better than him. When he goes to El Hazard and assumes control over the Bugrum, Jinnai is finally allowed to shine and he's surrounded by people (er, bugs) who don't know he's an orphan and don't know he has nothing. He can finally be more than what he is.
More poignantly is the fateful night Makoto first meets Ifurita. Fujisawa-sensei also appears to be living at the school and Nanami brings him refreshments. What is a teenage girl like her doing out in the middle of the night like that? It could mean that she doesn't live far away and is making a quick visit before bed. Then there's Makoto and Jinnai, and Jinnai's hilarious attempted murder of Makoto. It doesn't even look like they left the school. And why would Jinnai lure Makoto to the school in the first place? Wouldn't killing him in a secluded park be easier? Or maybe it's because they're closeby to their living quarters and so it's more convenient for them?
It's also important to note the memories that Makoto gives to Ifurita so she won't be lonely. It's basically his own memories but altered so that she's integral in his life as well. All of these memories involve his life at school. Not one of these memories shows Makoto's parents, or his house. Since Ifurita means so much to him, wouldn't it make sense to give her some memories of his parents? Unless his parents truly are dead, and Makoto doesn't show them to her because of his own painful memories of them? So he shows her his school life because that is his present—his family essentially—and that is what makes him happy.
It would make sense as to why these three teenagers don't even think about their parents, or possible other siblings, while in El Hazard. If they really are orphans, then for them there's no point in returning home because all that remains on Earth are the reminders of what they've lost. Of course, this leaves the adult Fujisawa-sensei, and whether or not he has family. But for the fact that he lives at the school—possibly as the caretaker for the students living there—it's safe to say that he might have no other family either. Which is why taking care of his students means so much to him.