Up the Tigers
Not seen any that dont take up slots.
Most do take up slots but the odd one doesn't such as the Queens Favour Artifact and Llamrei Mount card amongst others.
I take it
"If a slot cannot stack multiple inventory does this apply to broken inventory items ?
and when waiting repair or can you wait until you repair them to make the choice?"
the answer is yes and No
No the slot is still full even though the item is broken. I guess you could consider the number of slots as your carrying capacity and so even though you longsword is bent you still have to handle its weight preventing you from carrying another weapon for example.
Somethings break the normal rules, like the stuff that doesn't take up slots, including, for example, one of the Artifact shields that is actually a "Special" and not a "Shield" and so goes in one of the Special slots so you need to make sure you check what it says on the card and to make sure where they can go.
(FYI, I know this is in the FAQ already, but if you have the Special shield you can still have either a Starter or Armoury card that contains the word shield in its title/description in your normal Armour slot)