"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.
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.
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.
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.