I see, fly guy eats time (literally) and can reverse time for specific objects by vomiting up time he ate. Assumedly vomiting on something replaces their current time by covering it with the time-vomit's time-period, causing the time reversal.
Tonfa's mental weirdness is caused by the aftereffects of setting back her time a day when she was transformed into a Kaiju. Her body and memories are out of sync causing a discrepancy due to a combination of being a living object and the amount of time reversed. Hence flyboy's creepy actions in previous chapters (trying to quick fix her) and his comments in this chapter suggesting that the Mage not consider using his time-vomit on the hero.
Riyo's healing might be a mixture of self time-stasis and transferring wounds to himself. The time-stasis might be reaching its limits judging from his conversations with fly guy, and that the Mage's head injury that he just healed is followed by Riyo having a sharp migraine shortly after and dropping his drink. This is also guessed off of the fact that Riyo is older than he looks, and fly guy mentioning he's incompatible with Riyo in a previous chapter (along with a portrait of Riyo overlayed on a assumedly stopped clock as flyguy says this).
Mage boy is seriously concerned that his presence is negatively effecting the Hero's purpose, and the Hero herself directly affirms that she has feelings for him but she is still being objective about him in terms of her being a Hero. Her refusing to dismiss him is because of his skills not because of her love. The Mage accepts this, and decides to use his feelings-normalizer/reset spell on himself again because he is actually affected by budding emotions towards her when he needs to keep being rational and objective. Judging from his last line, it's possible he's supposed to do something to her if he believes she can't continue as a hero.
Lord knows what futalady's problem will be, because this party is becoming a cluster fuck of a time bomb it seems.
Anyways, I think the author is trying to do show not tell, but is too discreet about it and compacting too many details at once. And flyguy's just super shady but essentially benevolent, I guess.