Objects don't have an AC unless time is a factor. See p. 246 of the Dungeon Master's Guide, under "Statistics for Objects", or the corresponding section of the basic rules:
When time is a factor, you can assign an Armor Class and Hit Points to
a destructible object. You can also give it immunities, resistances,
and vulnerabilities to specific types of damage.
However, to carry objects like armor, you need a strength score, and objects don't have attributes, per above. See p. 176 of the Player's Handbook, under "Lifting and Carrying", or the corresponding section of the basic rules:
Carrying Capacity. Your carrying capacity is your Strength score
multiplied by 15. This is the weight (in pounds) that you can carry,
which is high enough that most characters don't usually have to worry
And they as such cannot carry or wear anything.
So in the first case, yes the clothes can ignite, as dead objects cannot protect their clothes or wear them.
In the second case, while the AC bonus doesn't protect the corpse, if they attack the armor it will be harder to break. It isn't dodging, so you can freely attack areas not protected by armor. See p. 141 of the Dungeon Master's Guide, under "Magic Item Resilience":
Most magic items are objects of extraordinary artisanship. Thanks to a
combination of careful crafting and magical reinforcement, a magic
item is at least as durable as a nonmagical item of its kind. Most
magic items, other than potions and scrolls, have resistance to all
damage. Artifacts are practically indestructible, requiring
extraordinary measures to destroy.
So, it will be more difficult to hack through.
The shield guardian is a sentient creature with an intelligence of 7 and a wisdom of 10. It has no innate need to protect the bearer if dead, since amulets weigh something and so cannot be worn, but can at the GM's discretion perhaps based on how much it likes the bearer.