Do pet stats scale off your character stats?

I’m a Conjurer and I’m running a pet build. Let’s say I get a item that gives 50% fire damage. Does that 50% fire damage also apply to the Hellhounds fire attacks or just to me and any fire attack I may use. Does an item need to have the text “Bonus to all pets” for the pet to gain the stats from the item?

No, only those things written under pet bonuses add to pet and auras