Yeah, they all have different accents.
The leftmost one speaks Central or Stockholm Swedish. The second one has a northern accent, which often drops final vowels, and he says vet int’, hitt’ på nå’! instead of the standard vet inte, hitta på nåt!
I wouldn't say vill and will are false friends. to will means to wish or to desire. to will comes from the same word as att vilja. "Why will it happen? Because I will it to happen and I shall make it so."
I do agree that English to want (to lack, as in the proverb "Waste not, want not.") has largely replaced to will in many contexts, the one at hand included. I do wonder why this shift happened.
We still use ska/skall's English equivalent as in the Duolingo sentence sometimes: "What shall we do for lunch?" Historically shall was used for the first person while will was used for the second and third person, but that distinction has been lost.
So I would say vill and will are friends that don't keep in touch.
Yes, in the sense I want to…, we want to … etc.
If you're talking about what you want to happen or what you want others to do, you get att: Jag vill att du ska svara 'I want you to answer', Jag vill att det ska regna i morgon 'I want it to rain tomorrow' – but then this is a different sentence construction. You cannot have att with vill in sentences like Jag vill sjunga 'I want to sing'.
I wrote "What do you wanna do?", and it was denied. I think it should be accepted, although it's really colloquial and not in Merriam-Webster's dictionary (though it's listed on Dictionary.com). I've lived in the USA my whole life, so all my friends and I speak English natively, and we all use "wanna" instead of "want to"