I think this is due to the HQ-9's heritage from the S-300, back when the USSR was significantly lagging in terms of terminal guidance electronics, so they made up for this with a larger warhead. Of course, this resulted in a bigger overall missile.
No. More like those missiles are also sized for nuclear mission tbh. You see it's a common practice for Soviet Long range SAM's.. S-75, S-200 and naturally S-300P and S-300V may have nuclear mission in mind, this demand spaces and weight. The other consideration is increased charge to mass ratio to help against ballistic targets, producing faster fragment velocity and maybe carry heavier fragments, might not be help as much but as you see from 48N6 to 48N6DM/E3 for S-400, the warhead is only increase.
Terminal guidance etc.. well S-300P was significant departure from old Soviet practices. Monopulse, Phased array radar, use of solid state electronics. I suggest you read about Raspletin, the general designer for Almaz (used to be MKB Strela).
The only system you might be correct in your assertion is S-75/Sa-2 where the radar is a conical scan type. This subject to target scintillation phenomenon, as the radar "sweep" around the target it will illuminate different parts of it, creating scintillation or rapid change of observed RCS. This caused inaccuracy of the command guidance, thus necessitating large warhead for S-75 missiles.