Is it permissible to shorten the prayer (qasr) and what is its manner during times when the questioner is asleep, noting that he alternates work and residency between his workplace and his home every 15 days?

Shortening prayers (qasr) due to finishing work and seeking rest is not among the permissible excuses for qasr. If the stay at the workplace exceeds four days, then one is not allowed to avail themselves of the travel concessions, even if the distance between the place of residence and the workplace reaches the distance for qasr. Every prayer must be performed at its prescribed time. If one is overcome by sleep and misses a prayer, it should be prayed upon waking, based on the hadith: "Whoever sleeps through a prayer or forgets it, let him pray it when he remembers it." As for combining prayers (jama‘), some scholars have permitted combining prayers by way of taqdim (advancing the later prayer) if a person is tired and knows that they will not wake up for the next prayer.