i myself did the exact same thing!
i'd been teaching myself for a while and started noticing flaws in my own guitar [however it was a lot cheaper than a squier

] and i did/have been doing similar things. tuners and a new nut is a base you've already covered. adding more springs and tightening the bridge screws slightly to lock it down, you've clearly got that done. you can teach about intonation at the 12th fret... urm... dunno what to say, i'm afraid i may sound patronizing... urm... the new squiers have 10mm holes i believe so you won't have problems with a variety of tuners to pick. [this is turning into a mental checklist.]
i modded my synchronized bridge into a floating trem with screws, if you use beveled screw heads you can make the bridge more stable but still be able to use the trem perfectly well; if he changes his mind at all.
my advice seems kind of unhelpful...
eek
thinking... thinking
-intonation
-tuners
-nut
-bridge
he could learn about temperatures that the guitar is comfortable with [?] winding the strings in the capstans so they don't slip [?] stretching the strings to help them settle into a natural state [?]
restringing correctly is a common mishap. if you turn the tuners so the holes in the capstans face the bridge/are in line with the nut slots, run the top of the string through the top so the tip pops out the hole to face the nut. stick your finger on the side of the capstan and pull the string so it pressed up against your finger; that'll give the right amount of slack to wind with. grab the end of the string and bend it round the opposite side of your finger then tuck it under the string. give it a tug without losing the finger width space and bend the string back over it's self. give the tuner a couple of winds and you should see that the string has basically been tucked under itself as well as being slightly counterwound on the tuner.
i shouldn't use my own guitar as a comparison as the only things left on it [when the neck is finished] that are stock parts are the bridge, the jack plate and the body. squiers are well-built and shouldn't need such a radical makeover. i hope i haven't repeated things you already know. thanks for reading my ridiculous rant. have a good evening!