Re: despite and despite the fact that
I suggest you banish "despite the fact that" from your writing. It's wordy and adds nothing that a rewrite couldn't do better.
Despite your presence, I won't come.
If you have other "despite the fact that [sentence]" examples and you want to post a couple, I'll show you how they can be improved (at least in my opinion) by removing that phrase.
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.