Aladdin should also probably have at least 3 rogue levels

The most important thing to remember is, this is a silly joke comic. For the funsies and the japery.

However, in the specific: 5e Paladins can get their power source from anything (including "their own self-belief" - "a paladin’s power comes as much from a commitment to justice itself as it does from a god".) so a Paladin devoted to a Djinn would be completely fine.

Yes. I thought that was pretty obvious. All Knights Radiant would be paladins, with each order having their own specific oaths. Because each order already has it's own specific oaths and gain specific powers from swearing and abiding by them. It's probably the single most direct analog between 5e class and fantasy badass from another medium that you're going to find. Also Kaladin in particular has the "classic" paladin vibe of being Lawful Good and wanting to protect the weak, smite the evil, etc. Then there's the Skybreakers who would be the Lawful Stupid stereotype, basically worshipping law for the sake of law and insisting on brutal and remorseless execution of it to the letter in all cases and refusing to acknowledge any sort of extenuating circumstances whatsoever.

Also while I'm quite sure Sanderson was at least working on drafts for Stormlight well before 5e came out he did used to play a lot of D&D as well as some other TTRPGs. I've seen a post by him where he said he hasn't really played much at all since becoming a professional writer because he would feel burnt out telling stories for a job then trying to relax by telling more stories, which is why he switched to playing MtG to relax. I would say his magic systems generally tend to at least partially resemble and incorporate elements of game design and balance because they all have very specific capabilities and limitations (see Sanderson's Laws of Magic).

That's the funniest part!