Have Prophet Muhammad (PBUH) or his companions ever offered Qadha salat? Where in hadiths/Qur'an they are mentioned?
If it is approved by Prophet Muhammad (PBUH) then can one pray Zuhr qadha with 'Asr fardh?
Validity of Qaza Salah:
There are two kinds of salah falls into this catagory:
Regarding Type 1, you must pray the salah when you remember as soon as possible and there is no doubt about. I have added few reference for similar situation based on hadith(There could be more):
On the day of Al-Khandaq (the battle of trench.) Umar bin Al-Khattab came cursing the disbelievers of Quraish after the sun had set and said, "O Allah's Messenger (ﷺ) I could not offer the Asr prayer till the sun had set." The Prophet (ﷺ) said, "By Allah! I, too, have not prayed." So we turned towards Buthan, and the Prophet (ﷺ) performed ablution and we too performed ablution and offered the `Asr prayer after the sun had set, and then he offered the Maghrib prayer. - USC-MSA web (English) reference : Vol. 1, Book 10, Hadith 570
Abu Huraira reported that when the Messenger of Allah (ﷺ) returned from the expedition to Khaibar, he travelled one night, and stopped for rest when he became sleepy. He told Bilal to remain on guard during the night and he (Bilal) prayed as much as he could, while the Messenger of Allah (ﷺ) and his Companions slept. When the time for dawn approached Bilal leaned against his camel facing the direction from which the dawn would appear but he was overcome by sleep while he was leaning against his camel, and neither the Messenger of Allah (ﷺ) nor Bilal, nor anyone else among his Companions got up, till the sun shone on them. Allah's Messenger (ﷺ) was the first of them to awake and, being startled, he called to Bilal who said:
Messenger of Allah I may my father and mother be offered as ransom for thee, the same thing overpowered me which overpowered you. He (the Holy Prophet, then) said: Lead the beasts on: so they led their camels to some distance. The Messenger of Allah (ﷺ) then performed ablution and gave orders to Bilal who pronounced the Iqama and then led them in the morning prayer. When he finished the prayer he said: When anyone forgets the prayer, he should observe it when he remembers it, for Allah has said:" And observe the prayer for remembrance of Me" (Qur'an. xx. 14). Yunus said: Ibn Shilab used to recite it like this:" (And observe the prayer) for remembrance." - USC-MSA web (English) reference : Book 4, Hadith 1448
Qatada reported it on the authority of Anas b. Malik that the Messenger of Allah (ﷺ) said:
When any one of you omits the prayer due to sleep or he forgets it, he should observe it when he remembers it, for Allah has said:" Observe prayer for remembrance of Me." - USC-MSA web (English) reference : Book 4, Hadith 1457
Regarding Type 2, as you might already know we are not allowed to and there are very few unique instances when we are allowed to knowingly miss a salah. But lets say we missed one for some work and want to perform the Qaza prayer, based on my personal research(Warning: I am definitely not an expert) there is something called Qaza-e-Umri. It means estimating all the prayers in one’s lifetime and then making them up. I personally could not find any hadith and quran reference for this type of prayer, moreover I found conflicting Information regarding its validity according to different Madhab. But it is a common practice in some countries(like mine Bangladesh).
Moreover, there is a community question "Does a Muslim have to pray all the prayers that he left out?" worth looking into, but I would add that even though this question has accepted answer I personally wasn't satisfied with any of the answers since even including the links provided I could not find any hadith/quran referencing this. Moreover answers are conflicting even with the links e.g. top two answers contradict on whether or not majority of the Muslims accepts Qaza Salah.
How it is perforemd:
(Cound not provide hadith/ quran ref but added my source) Only the prayers which are Fardh and Waajib need to be make up for missed prayers. And the prayers to be performed as This: The Mode of Performing Qada.
Inschallah I will update the answer if I find better one. May merciful Allah forgives us for our missed prayers.
There is no place in the Quraan that really steps the prayers or its timings as far as my knowledge goes. These things come from Hadith (aka. What Prophet did and showed), the logic of Fardh is to show how important and followed it was.
if you are uncertain to be able to catch the Asr prayer... you can do Jam3 (joining) with the Duhr prayer. Prophet did once pray in advance, when they were about to travel, and the travel plan cancelled, and he didnt go back and prayed.
This is from my questioning of "people of better knowledge", and my understanding when i questioned how and why Shia muslims always tend to join prayers, so this is the legality to it (to my perception).... open and wanting to learn better...
As for "why not always do it"?... The prayer has been prescribed to you as a timely thing (in the Quraan)... so technically cannot really do that, to my understanding, but obviously there is much i am not aware of, and always can learn...
PS: Answered to the best of my knowledge. Just a normal "born Muslim" knowledge, no depth knowledge to exact citing