Praise be to Allah.
There is no basis for what you mention, about the verse that one’s eye falls upon when opening the Mushaf being regarded as a message from Allah, and it is not prescribed to seek omens in the Mushaf. The scholars have stated that this is akin to what the people of the Jaahiliyyah did of seeking divination by means of selecting arrows.
Similar to that is what you mention about putting verses in a box and choosing a verse every morning. The Muslims have no need of such folly and imitating the people of Jaahiliyyah.
Al-Qarraafi (may Allah have mercy on him) said: With regard to seeking omens, at-Tartooshi said: Seeking omens from the Mushaf, geomancy, drawing lots, throwing grains of barley and “reading” the patterns it falls in – all actions of this type are haraam, because they come under the same heading as seeking divination by means of selecting arrows.
Divining arrows were sticks that were used during the Jaahiliyyah. On one was written “Do it” and on another was written “Do not do it”, and on a third was written “Neither”. A person would select one of them, and if he found on it the word “Do it,” he would go ahead with what he wanted to do. If it said “Do not do it”, then he would refrain from it, and believe it to be bad. If he selected the arrow on which was written “Neither”, he would select one again.
Thus he was trying to find out his fortune from the unseen by means of these sticks; if he found that his fortune was good (according to the stick he selected), he would go ahead with his planned action, and if he found it was bad, he would refrain.
Similarly, the one who seeks omens from the Mushaf believes that if it shows something good, he will go ahead with his planned action, and if it shows something bad, he will avoid doing that. This is exactly the same as seeking omens from divining arrows, which the Qur’an states is haraam, so this action [seeking omens from the Mushaf] is also haraam.
End quote from al-Furooq (4/240).
See also the answer to question no. 145596.
It says in Mataalib Ooli an-Nuha (1/159): Seeking omens in the Mushaf was something done by Abu ‘Ubaydillah ibn Battah, but Shaykh Taqiy ad-Deen [Ibn Taymiyah] and other leading scholars did not think that it was correct.
It was narrated from Ibn al-‘Arabi that it is forbidden. Al-Qarraafi narrated that view from at-Tartooshi al-Maaliki. The prevalent view in the Shaafa‘i madhhab is that it is makrooh (disliked). End quote.
One can benefit from the Qur’an only by reading and reciting it, reflecting upon its meanings, and acting in accordance with everything in it.
And Allah knows best.