Short answer; treated like a PC in this case
A hobgoblin has an AC of 18. It is 16 base AC for the chainmail, +2 for the shield. Being heavy armor, the chainmail does not let the DEX bonus to be added. If it removes the shield, it goes to AC 16. If the chieftain uses plate armor and shield, its AC would be 20.
Yes, your assumptions are correct.
When equipment is listed under the creature, it means it is following the rules for characters regarding that equipment.
Goblin archers have different game stats from a goblin foot soldier.
If a creature is somehow capable of equipping gear, and finds suitable gear for their body shape, you can change the stats of a particular creature to fit the new equipment.
It makes no sense if a goblin chieftain has a plate armor that can fit him in his tresaury but he still uses the same old ragtag armor as his foot soldiers. Same goes for weapons. If there is a magical sword in the treasure stash, probably the chieftain is wielding it.
This can be used to flesh out and give more color to the campaign. Suddenly the +1 longsword is not just some randomly rolled piece of game statistics. It is the "Sword of Uklangor", the goblin chieftain. Some of those creatures can even have class levels.
 I don't recall if Uklangor was a goblin, sorry if I made a mistake there.