the burning heart buff is applied while you have a draconic skill "active"

because inhale is basically 2 instantaneous hits (the first instant one, and then the delayed instant one), i dont know if its counted as being "active"

talons may give you the buff as it is "active" on enemies for a few seconds, but the most reliable things to get this passive is spiked armor (and morphs) or dragon blood (and morphs) as those have fairly long duration self buffs

as far as im aware, "healing received" buffs any healing effects that are applied to your character, including self healing

"healing done" improves the value of heal skills that you use, regardless if they are applied on you or another player

so if this is all true then any heal which affects yourself is affected by both "healing received" and "healing done"