Ok as you might be able to tell after this post, I'm relatively into Gundam.
The reason they don't use bombs is because in (at least the original timeline, most of the recent Gundams have much much less justification) Gundam they have such effective EM Jamming and Interference that Radar guidance is useless beyond a few meters, IR is fuzzy as hell and impossible to accurately target and even Visible Light gets a slight foggy effect, also any kind of useful autonomous computer in a missile in a combat zone would need enough shielding that it would be as big as the GN Sword IIIs that the 00 Raiser Gundam is holding in his hands, minimum. All combat for at least the early days in the Gundam series takes place in Visual range only because of this.
The reason to then use mobile suits is then:
1. They were designed primarily for space, the exact shape doesn't matter there and they have the side effect of still being usable on Earth.
2. The mobile suits aren't controlled exactly, most of the movements are preprogrammed, a humanoid shape makes it pretty easy to just motion capture somewhere for the movements.
3. The mobile suits run on mini-fusion reactors, but they are still too big when they were first made to fit into a fighter jet sized spaceship.
4. And then the reason for using mobile suits over basically space tanks is umm, there isn't a reason they use both and the space tank type stuff (Mobile Armours) is almost always shown as being better (But of course only used by the enemy so the good guys have to struggle against the superior odds).
5. The moving limbs help in space for adjusting momentum.
Also the skirt thing is because the gundam's design has small similarities with Samurai Armour, which does have a skirt-like piece of armour.
Personally I think the original Gunadm series had a lot more solid sci fi foundations and ideas that make more sense than a lot of other sci fi tv series (Of course a lot of it was made up on the spot and occasionally retconned in the original series, but they've stuck with it consistently, all the way to Gundam Unicorn that's still releasing now). There's tons of examples of this if someone wants me to get into it.
TL;DR: There's a bunch of in-universe explanations in Gundam that make it make a lot more sense that if you just assumed it was the world as it is but in the future.
