Assalamu Aleykum Warahmatullahi Wabarakaathuh sister Hannah. Jazakellahu Kyran (wa Barakallahu Feeki bi alfi me atin) for the video, it was a real heart breaker (especially when I read it for the first time two years ago), May Allah (SWT) forgive us for our sins and increase us in our Wala' (Loyalty and Love to Allah [SWT]) and Bara' (Dislike for all that which Allah (SWT) hates/dislikes), Ameen. As for your question sister, the referances of these poems comes from three main sources:
1.) Thorough Explanations of the Quranic verses and the Ahaadith by renown scholars (Abu Haneefah, Ahmed ibn Hanbal, ash Shafi'ee, Malik ibn Anas, Ibn Taymiyyah, al Qurtubi, an Nawawi, etc. (Rahmatullah Aleyhim
Ajma'een) and most importantly, the scholars of the Shahabah (RA) like Ibn Abbas, Abdullah ibn Masid, Hasan ibn Thaabith, Anas ibn Malik, etc.)
If one were to read the books of Tafsir and Aqeedah by the Four Imams (Abu Haneefah, Malik ibn Anas,in ash-Shafi'ee, and Ahmed in Hanbal Raheemahumullah), Ibn Kathir, al Qurtubi, and Ibn Taymiyyah, then they would find all the Ahaadith and Descriptions of Jannah and the Akiraah (for example, if we were to read the Tafsir of Ibn Kathir (RA), and if we went to the Tafsir of Surah Qiyaamah, we would find the meanings of the
verses, and also with Ahaadith also.)
2.) Quran:
The poem describes:
a.)the drinks of the people of Jannah (and thier vessels) and food
b.)the spouses (and clothing)
c.)their lovely faces (which will be shining)
The Surahs (that these topics are mainly mentioned) can be found in: ar-Rahmaan, al Waqiah, ath Thoor, Qaaf, al Qiyaamah, and al Insaan.
3.) Authentic Ahaadith
If you have an English copy of Riyadh as-Saaliheen (by Imam an Nawawi), there are many (large) Ahaadith that mention the Akirah (Hereafter), and towards the end of the book, there are about 2-4 Ahaaditho (from Bukhari and Muslim) that mention the day that Allah (SAW) will remove "His Covering" and so all of His Creation will see His Face, Exalted and Mighty He is.
**"His Covering" reffers to:
a partition of of beautiful and pure light (that does not resemble any type of light that one has seen in this world) that one would be able to see if they were to look up at Allah (SWT) (in Jannah). Only during the "Day of Increase" will the covering be gone, and by that, the Inhabitants of Jannah would be able to see Allah (SWT)'s appearance clearly and accurately, instead of seeing the pure light of "His Covering."
***"The Day of Increase" refers to:
not a day, but a moment in time in which (as the poem explains, that the People of Jannah will see the Appearance of Allah (SWT).
That makes sense too, because whenever Allah (SWT) or Rasulallah (SAW) talk about a "Day" in the Hereafter, it does not refer to The Day of 24 hours, but the "Day/Time" in which an important event will take place.
Example:
The term, Yawm al-Qiyamah literally means, "The Day of Resurrection (Doomsday for the Evildoers), but in Suratul Ma'arij (Chapter 70), Allah (SWT) described the Day of Resurrection to be "equal to fifty-thousand years," and also, in an Authentic Hadith (I believe it was in Tabarani), Rasulallah (SAW) stated that "a day in the Hereafter is equal to 500 years (of the Duniyah)."
And Allah (SWT) knows best.
Jazakumullahu Kyran***********