So I play a few of the elemental races (ifrit, Sylph, Undine) but one thing I never thought of till now is whether I have to pay barding for armor. Technically speaking they look humanoid in shape but they are not of the humanoid species group.
I say no, your armor/clothes don't care about your metaphysical biology, just your shape, which is no stranger than a dwarf, kobold or gnoll.
Agree. This is one of the cases where "humanoid" refers to general shape rather than type.
It might not be a bad idea from a campaign perspective to use the "armor for unusual creatures" rules for any creature whose body shape is extremely unusual for the area. This might even catch some humanoids if they're sufficiently odd in proportions or have extra appendages. Conversely, if you're in a metroplis in a nation of kasatha with very few non-kasatha inhabitants, I'd expect human armor to be expensive to purchase but kasatha armor to be "normal"-priced.