We don't use "of" after "despite." You could say "In spite of all this..."
Shouldn't "Despite it all, I am happy" be accepted? Considering the ambiguity of זה meaning that/it as well as this?
I disagree with @NaftaliFri1, the general meaning of the sentence is the same, but "Despite all this", "Despite all of this" and "In spite of all this" are much more accurate translation (because "despite every thing" is "למרות הכל" "while the examples means "למרות כל זה")
To elaborate on your point: "Despite all of this" implies you're referring specifically to what you just said, whereas "despite everything" keeps it more open-ended. Still, while I agree that it is a more accurate translation, this is a Hebrew course, not one of semantics, after all, and this sentence does come void of context, so we want to make the experience as focused for the learner as possible. If somebody translates it to "everything", they obviously understand the sentence and should not be penalised.
Well, לַמְרוֹת is originally the contracted form (לְהַמְרוֹת -> לַמְרוֹת) of the infinitive of the Hiphil הִמְרַה to defy, which is used in Is 3.8 לשונם ומעלליהם אל יהוה למרות עני כבודו their tongue and their acts are against YHWH, defying the eyes of his glory. But having become a preposition now, it can only be followed by a noun (בָּא רַק לִפְנֵי שֵׁם), not a suffixed prononun.