Sura Yasin

"The sun runs to a resting place/stopping point/stopping time (mustaqirr) of its own. That is the decree of the Mighty, the Knowing." (36:38)

Clasically, the sun's "resting place" has been taken to mean: (a) the sun disappearing after sunset (just as a human being goes to their dwelling place at night before rising in the morning), (b) the final destiny of the sun on the Day of Judgment, or (c) the solstice, in a reference to the sun following its winter and summer orbits until the solstice.

Today, some Muslims interpret it as referring to (d) the astronomical end of the sun/the solar system.

Personally, I tend to see this as a poetic or celebratory expression of the natural world, than a statement intended to inform people of a scientific fact (even if the Qur'an is consistent with facts of reality).

In any case, options (a), (c), and (d) match scientific understanding (obviously, from the perspective of earth, the sun rises and sets).

Option (b) is outside the domain of science since it pertains to the end times and hereafter which no longer operate according to the natural laws presently.

(Some people seem to be of the view that it is unscientific to say that, from the perspective of an earth observer, the sun rises and sets. Perhaps people do not go out and watch sunrises as often as they used to; however, I would challenge them to explain why it is unscientific to discuss sunrise and sunset, when this has such a gigantic impact on things such as the weather and ecology, not to mention basics such as timekeeping. So it is scientifically fine to discuss the sun from the perspective of an earth observer, or from the perspective of right outside the solar system, or from an intergalactic perspective; they are all just viewpoints.)

As for "running", this matches the idea that the sun has a motion in the galaxy/universe and is not fixed in one spot, although it also matches the idea that the sun moves along the sky from the perspective of an earth-based observer. So either perspective is correct with respect to reality.

So the verse is open to several interpretations but they do not conflict with what is known about how the universe and natural world works. Probably the main point is to inspire reflection on the natural order.

"He is the one who placed fire in the green tree, from which you kindle it." (Qur'an 36:80)

(Of course, in any translation, there is always some involvement and interpretation from the translator.)

According to 'Allamah Tabataba'i in Tafsir al-Mizan:
 

This verse aims to dispel the notion that it is impossible to bring life back to something lifeless. Life and death are two opposites. The response is that this is not possible because God has made green trees, which drip dewdrops, a source of fire which people light. Exegetes say that "tree (shajar)" refers to two specific types of dry, bushy, desert shade-trees called shajara al-markh and shajara al-ʿafār.   Their  wood is collected while still green. Then, the branch from the markh tree is struck atop the branch of the ʿafār tree, and fire is kindled, by the permission of God. Restoring life to the dead is no more wondrous than kindling fire from a green tree, for both examples involve opposites. [End quote]

Sunni exegetes also have a similar view regarding the two trees that are being referred to.

To my knowledge, Shajara al-markh correponds to Leptadenia pyrotechnica, a brushy, short desert tree found from Senegal to India. Shajara al-ʿafār corresponds to a many-branched shade tree found in Ethiopia, Yemen, and Saudi Arabia, which can grow quite large. The name can be used for several species of tree including Tarchonanthus camphoratus.

Of course, Qur'anic verses can and do have multiple meanings (in hadith, we are told there are layers of meaning). This is the meaning that is most readily apparent from the text. 

"Imam mubin" ("manifest imam", "clear imam", or "clear record") is generally understood to refer to a divine record in which all things and divine decrees are inscribed.

(Some exegetes have explained that it is called the "imam" of divine records because it is the highest of the books, hence the leader of books, as opposed to lesser divine records, such as individuals' scrolls of deeds.)

Some hadith also say that the "imam mubin" is Imam Ali. In one hadith, Imam Ali is quoted as saying that, "I am the imam mubin. I distinguish between truth and falsehood, and I have inherited this from the Messenger of Allah."

Perhaps both views are correct, in that it is possible for Allah to provide any of His servants with knowledge of all things.

Some hadith offer explanations for the circumstances of revelation for this verse. However, they do not relate to the phrase "imam mubin" but rather refer to why the previous phrase ("what they have sent ahead and their effects [which they left behind]") might have been revealed. These relate to the community in Medina as well as the general idea that people are rewarded or punished after death for the good or bad practices or legacies they have left behind. However, they do not say anything specific linking the word "imam" directly to the occasion of revelation. I am not aware of any hadith that do this, although there may be some!