a) Bacterial in-line filters are hydrophilic, and should not be used with a humidifier.
b) The humidity in SG is always above 80%, which is what most humidifiers target, hence, in my opinion, it doesn't make much difference unless you sleep in an air-conditioned room. For me, I only use my humidifier in winter when the air is a lot drier, and only use only when necessary as I'm generally lazy and dislike having an additional thing to wash/clean/dry daily. But mainly, because I like to use an additional in-line anti-bacterial filter, which can't be used with a humidifier.
c) If you have condensation in your tube while running a humidifier, a heated tube and/or an insulating wrap around your tube could help reduce/eliminate it.
ResMed's climateline heated tube contains a sensor at the end, to help maintain a constant temperature even if the ambient temperature in your room changes significantly over the course of the night. This usually happens in countries with 4 seasons, and not so much in SG, where the temperature tends to remain pretty constant all night long, all year round),
d) If you open your mouth while you sleep, air will "leak", and your AHI will be affected. Either try using a full face mask, or look into using a chinstrap to keep your mouth closed.