When it says "treated as medium armor" it means two things;
First, you must be proficient in medium armor if you want to wear an armored kilt with a light armor.
Secondly, it means you should treat it like you are wearing a medium armor such as a breastplate which means your speed will be reduced. However, barbarian's fast movement works with medium armor which means your speed will be 30 ft(Assuming you're not a Dwarf, Gnome or Halfling) instead of being normally reduced to 20 ft.
Medium or heavy armor slows the wearer down. The number on Table:
Armor and Shields is the character's speed while wearing the armor.
Humans, elves, half-elves, and half-orcs have an unencumbered speed of
30 feet. They use the first column. Dwarves, gnomes, and halflings
have an unencumbered speed of 20 feet. They use the second column.
Remember, however, that a dwarf's land speed remains 20 feet even in
medium or heavy armor or when carrying a medium or heavy load.
It should be noted that Speed column in armor and shield tables show the speed when you only wear that armor. An armored kilt on its own is a light armor and so is a chain shirt. Individually those don't slow you down but if you wear them together chain shirt + armored kilt becomes a medium armor that weighs around 35 lbs which is heavier than most of the medium armors and it slows you down like a medium armor.
About the maximum dexterity bonus Dancing Kobold's answer is correct. You should use the lower maximum dexterity bonus.