"Alys never figured it out. I paid her my wedding fund in order to stay with her, but she went and bought me armour worth ten times that so I could keep up in a fight!" - Hahn,Conversations Within Elsydeon
It's actually consistent with how Rune mentioned Alys fought for more than just money. It's not unlikely Alys was merely attempting to provoke Hahn to stand up for himself, but Hahn never caught on to that.
Since the Academy never pays up for the monster extermination in the basement, charging Hahn every step of the way might have been her idea of an alternative payment program.
She may have had a bit of a crush on him, and squeezing Hahn for money was just her way of affectionately picking on him. She does seem pretty alarmed when he says he's got a fiancee.
Chaz is the only one who freaks out that the emergency shuttle is crashing. He's the only person in the group who has never experienced or studied space travel before: Wren is an android, Rika is his student who's lived in a lab all her life, and Rune remembers the spaceship Noah and going into cryosleep.
Techniques are different from magic, but it's never really explained how. That's because the difference is in the name. They're techniques as in jutsu, like any ninja story ever: special combat abilities that can be taught to anyone and are generally grouped by tradition (the Res family, the Sar family, the Foi family, etc), with some people having an innate affinity for some and no ability with others. True magic is made up of Skills that seem to be taught through a combination of asceticism and book study, and can only be learned by those with Esper blood.
Why does the "Destruct" combination attack include Deban, a defensive shielding spell? To contain the damage. Destruct includes all the most powerful non-melee attacks the non-optional characters have, but Rika has only melee combat Skills. She can't get that close to all that energy safely, so instead she uses Deban to keep the blast centered on the target.
Why does the Profound Darkness kill ordinary people with its presence, despite the Black Wave not being a form of detectable radiation or poison? The people of Algo were literally created by the Great Light from its own power, so the power of the Profound Darkness is anathema to their very being.
Of course you have to run away from the carnivorous trees. They're trees! What are they gonna do about it? Chase you?
Why does Zio capture Demi instead of killing her? Because he's a Squishy Wizard who directly siphons power from Dark Force. The only spell he uses without summoning the Nightmare is his petrification curse, which won't work on Demi because she's a machine, and he can't just crush her because she's the central control of Nurvus; if he destroys her, he has no way of knowing what parts of Nurvus' functionality will be compromised or what the system will do in response (he obviously has no idea that Seed is fully aware that Demi has been captured and has sent help through Rika), and being entirely mechanical, he can't use magic to control her mind or brainwash her like he does with his cultists.
Motavia is nothing but desert despite being covered in oceans. Well, yeah: installing those oceans was part of Mother Brain's terraforming efforts. In the second game, Motavia is lush and green all over, but a thousand years later, it's all arid scrublands and minimal forests, and there's no domed terrarium farms anymore. Motavia's drying out because its atmosphere can't maintain a water cycle without the environmental control systems enforcing it. That's why the quicksand is spreading, too: if the atmosphere can't hold water vapor, it's eventually either going to stay in the oceans, or get absorbed by the earth.
Chaz is one of the few examples of an RPG protagonist who isn't completely comfortable with looting strangers' houses for whatever he can find. It's not just a personality quick, though: he was the leader of a gang of kid-thieves before A Lys took him under her wing. He refuses to go through other people's things because he left that life behind when he became a hunter. Either that, or Alys whupped the habit out of him.
Raja got exiled, but if you talk to the NP Cs who actually know and have heard of him, they all describe him pretty favorably. Gyuna even points out that Raja was tricked by those who were jealous of him. It seems weird to be jealous of the weird old guy who tells bad jokes, but the fire-worshiping religion is also the Dezolisians' only government. Raja's an excellent priest, but he's way too laid back to be much of a politician; most likely he was sent away to be the head of a distant, backwater church because he had political rivals who couldn't get him out of office any other way.
The climate control system never gets repaired. Wren and Demi are prepared to help it limp along for as long as they can, but they acknowledge that it'll never work again and Motavia will return to its native state: a completely arid desert that was never meant to support Parmanian life.
This isn't necessarily true. Though Motavia had regressed in its terraformation since Phantasy Star II, there were many factors that contributed to the environmental crisis. Without Mother Brain, a lot of the AI systems on Motavia went rogue, thus causing the de-terraformation. Not to mention Zio had been deliberately screwing with the control systems as part of the will of the Dark Force. He knew that if Motavia went back to its normal stasis that all Parmenians would die on the planet. As for the Motavians, he was slaughtering them outright. By the end of the game though Zio is dead, and every AI system on Motavia has been dealt with. They had also effectively destroyed the Profound Darkness once and for all. Wren and Demi implicitly state that everything will be fine. Motavia won't go back to being like it was in PSII, but it's not going to get any worse with climate systems stabilized and their monitoring the planets from Zelan. And they plan on monitoring Motavia until it's able to properly sustain itself. This isn't going to happen overnight, but it will happen on Motavia. Not to mention they keep the Landale, so if things screw up on Motavia again they just need to fly back down there and fix it again.
The environmental system was slowly declining long before PSIV. Mother Brain's destruction meant the system started to fall apart, and Wren has been doing his best to take care of it ever since; at the end of the game, Wren and Demi are prepared to maintain the system as long as they can, but it's been in decline for a thousand years, even when it had active caretakers with full control. This is a large part of what Wren's conversation with Daughter means: that human life can endure conditions that their technology estimates would be insurmountable. The system will eventually fail, but humans will find a way to struggle on.
Every time Chaz is alone, he's looking for Alys. Once in the intro, once at the Academy, and again at the Anger Tower. The final time, he's looking for Alis. It's a subtle nod to his search for answers and guidance for pretty much the whole game (and possibly his entire life).
Wren is 998 years old, meaning he was built two years after the destruction of Mother Brain and the defeat of Dark Force in Phantasy Star II, which means he was also built after Parma was destroyed. He's the top AI in existence, he basically has sysadmin privileges for the entire solar system, and he has sufficiently sophisticated programming that he developed emotions. With no Mother Brain to rule the system and no Parmanian scientists to develop him and with the Daughter project being on the books but incomplete, who built Wren? It was probably Dark Force. Wren is sophisticated enough that building him, as a highly-specialized custom Wren-type android, would have taken a while. Dark Force had just destroyed Parma and gained the ability to spawn multiple expressions of itself in Algo, and there was already one on Kuran by the time Chaz and company got involved. At the end of Phantasy Star II, the only creature in the system that had any reason to build a customizable and heavily-armed android capable of overriding every directive in the environmental control system (particularly the Climate Control on Dezolis and the Plate System on Motavia) was Dark Force itself...
If Chaz and company don't take the Silver Soldier mission, someone else does, but that person is never going to solve the mystery because they don't have an AI in their party. Since the mission becomes unavailable once Demi leaves Nurvus, that means that once Daughter determines that SeeD is out of commission, she's still going to attack the other installations on Motavia (and Dezolis, if she can manage to extend her reach that far) but with no one in direct control, no one is going to know about it until Wren or Demi specifically checks it out. That's why you can't enter the Fort if you don't take the mission: Daughter is the highest-ranking AI in her understanding of the system, and although she has no network to reach the others, she has full control over her own facility... and there's no way past the laser array that is unavoidably deadly. Even Wren and Demi won't touch it. If you don't take that mission, Daughter is going to cause a lot of problems for the already-crumbling environmental control system.
Less horror, more tear-jerker: Very early in the game, Alys criticizes Chaz because "his swing is too slow". Cue Chaz's gaining level 13, where he learns Airslash, the skill where he swings his sword so fast that the vacuum left in the wake of the blade causes damage to every enemy on the screen. Unless you put unusual effort into level grinding, Chaz will generally get there right around the time Demi joins the party. It's actually the last thing Alys says to him as a teacher. After leaving the Academy, she's still the unopposed party leader, but she doesn't have anything else to say about his skill as a combatant. He was working on it the whole time, and finally mastered it just as he lost his mentor.