Is it permissible for a sick person who cannot sit to combine and shorten prayers, and is he required to make up the prayers he performed in this manner?

Combining two prayers is a concession for the sick according to many scholars. However, it is more prudent for him to perform each prayer at its appointed time or to combine them nominally (جمع صوري). As for shortening the prayer (qasr) for the sick, this is not permissible according to any of the scholars.