Yes. There is no special provision that undead cannot benefit from armor. Undead are proficient with any armor they're described with in their entry, and shields if they're proficient with any armor.
As such, a skeleton animated by this ability is proficient with light armor and shields (due to their entry).
Zombies are not described with any armor, and thus are not proficient with any armors. They can still wear armor, but they suffer non-proficiency penalties (the armor check penalty to attack rolls). It's a good idea to still equip them with armor that doesn't have an armor check penalty, such as leather armor or masterwork studded leather.
Ok, good! So i can assume an skeleton could wield any weapon from the martial weapons list, since it can use a scmitar. Right?
Unfortunately, no.
Proficient with its natural weapons, all simple weapons, and any weapons mentioned in its entry.
They'd be proficient with simple weapons and scimitars. You could ask your GM if you can make it proficient with better armor or a different weapon, since the skeleton entry is really just an example for a skeleton raised from a 1 HD humanoid. That, or you'll need to raise it from a creature with better proficiencies.
A skeleton is proficient with any weapon the base creature was proficient in. Same for armour.