Happosai is canonically unable to bring himself to hurt children, even in the manga. Then again, his kind of help towards children can be very questionable, but he's actually far better than Genma (who would steal food from his own child and submit him to actual physical torture) in that regard.
Concerning Keitaro teaching 3-A, eh. Without Negi's interest on Kyoto, he'll never see a reason to insist the school trip to take place there, so no Kyoto arc, Setsuna probably never comes close to Konoka. Eva has no reason to reveal herself as a vampire, so Keitaro never gets any training from her and, if this role replaces his one as Hinata's caretaker instead of taking place after it, he doesn't even get training from Seta. Takahata is probably too busy to teach him anything in the way of fighting, and Takahata is no mage anyway, so he probably falls under the tutelage of Yuuna's father or Gandolfini (the dark skinned mage who worked with Takane and Mei) instead.
Knowing Keitaro's proclivity for stripping accidents and the fact he wouldn't be rooming with 3-A's students like Negi, he would probably end up with Takane as his Naru. That assuming he doesn't have the Toudai obsession anymore; if he had it I see him just trying to get out of Mahora and into Toudai, which only pulls him further away from the Negima cast whether he succeeds or not.
Does Chao still exist? No Negi in Mahora probably implies she never comes into being in the first place. If she still exists, Keitaro is no match for her and no way he's formed an Ala Alba to stop her, so she successfully reveals magic to the world. Being a complete newbie, Keitaro is probably spared being turned into an ermine, but his tutors in magic, Takane included, probably are, and unless her punishment is only temporary, that just drives him further down. No Ala Alba means no trip to Mundus Magicus, and while the mages of Earth are too busy with the aftermath of Chao, or even if they're just otherwise oblivious to Fate in the Chao-less alternative, Fate and Cosmo Entelecheia succeed without any real opposition and seal the Magical World into suspended animation. On the plus side that means the Mars versus Earth war never comes to pass in the future.