I believe those stories are false.

Yeah, there are verses in the Quran that basically describe a flat earth.

Muslims dismiss this saying that it’s being figurative, but for a number of reasons I know that is falsez

Ah, yeah, this one is easily provable wrong, unless you're a flat-earther, I guess x)
In this verse, is the flat-earth described by a human, or a prophet/god ? Because if it's a human it can be chalked up to the fact that they didn't know, if it's god-told... well god is wrong x)
Anything else worth knowing ?

Yep, it is definitely god speaking. It’s on 18:86 of the Qur’an, which says:

“Till, when he reached the setting-place of the sun, he found it setting in a muddy spring.”

Now Muslims would say that this isn’t a literal sun going into a muddy spring, but rather the sun setting on the horizon into a black lake. There’s no difference between the words for lake and spring in Arabic and the word for muddy here also means black, so this could very well be talking about the Black Sea, although they didn’t call it that back then.

This is obviously false to me though, because the Qur’an elsewhere speaks of the sun journeying to its setting place elsewhere in the Qur’an and Muhammad commented on this verse saying that the sun asks permission to rise every morning.

So, the question you have to ask is, where is the sun when it is asking permission to rise? The truth is, it never rises, so any answer to the question leads to a flat earth.