I looked in the translation by Abdullah Yusuf Ali, "Towards Understanding the Qur'an" by Mawdudi, a small translation by two muslims whose names I have forgotten (but their translation reflects some famous tafsirs and sources of ahadith), and, lastly, my (new) Arabic dictionary. I found that Mawdudi's tafsir and the Arabic dictionary to be the most comprehensive in giving information about this subject matter (second, of course, to just plain reading the Qur'an).
Those verses are talking from Dhul-Qarnayn's perspective of where the sun set/rose. Dhul-Qarnayn found the sun setting in a murky spring, and Dhul-Qarnayn found the sun rising on a certain people. Allah gives His factual descriptions BEFORE describing how Dhul-Qarnayn found where/when the sun was setting/rising.
Until (Hattaa) as (idhaa) he reached (balagha) the place or time of sunset/west
(maghriba)... (18:86)As (idhaa) he reached (balagha) the rise/time of rising [of
celestial bodies]/break [of day] (maTli`a)... (18:90)
To further explain: just like Morocco is called Al-Maghrib (the West) and we have a prayer at sunset time called maghrib (the "a" on the end of the word in the verse is a vowel denoting accusative grammatical case) and maghrib is used today even today to mean the direction west.
The key here is that Dhul-Qarnayn found the sun setting in a murky spring. The verse is very explicite in showing that the setting of the sun (and the rising) are from Dhul-Qarnayn's perspective.
Knowing this information, we can understand the description of where the sun set and rose (from Dhul-Qarnayn's perspective) to be simply human descriptions of the areas (both westerly and easterly) of Dhul-Qarnayn's reign.
I hope that clears it up.
As for Dhul-Qarnayn being Alexander the Great, that is only speculation at best. So don't jump on accusing the Qur'an of what it does not say. Some scholars say it was Alexander the Great, but some scholars may be wrong sometimes too. They are not prophets. Muslims are warned not to follow blindly. We are taught to seek knowledge and correct our brothers if they do wrong. Know this, at best the answer to the question of who is the personage of Dhul-Qarnayn is simply speculation. Having said that, I know some scholars say it was King Cyrus, the Persian Emperor, who is described in the Book of Ezra as a God-fearing king who liberates the Israelites because he is such a God-fearing individual. (source: Mawdudi's "Towards understanding the Qur'an") Additionally, Mawdudi writes, "Nevertheless, the information available to date does not enable us to form a definitive opinion concerning Dhul-Qarnayn's identity." God knows best.