How many Rakats are there in combining Dhuhr and Asr prayers, and Maghrib and Isha prayers, both when traveling and when at home, and what are the proofs for that from the Quran and Sunnah?

It is permissible for a traveler, once they have left the inhabited area, to combine the Dhuhr and Asr prayers, and the Maghrib and Isha prayers, and to shorten them. Shortening is preferable. The Maghrib prayer is always prayed as three rak'ahs. The permissibility of combining prayers during travel has been adopted by the Shafi'is, Malikis, and Hanbalis. As for combining prayers while at home (not traveling) without the excuse of rain, it is not permissible according to the majority of scholars. However, some scholars have allowed it due to hardship, citing as evidence what the two Shaykhs (Bukhari and Muslim) narrated from Ibn Abbas, that the Prophet, peace and blessings be upon him, "prayed in Medina seven and eight [rak'ahs]... Dhuhr and Asr, and Maghrib and Isha." Ibn Abbas said: "He intended not to cause hardship for his Ummah." If one combines prayers while at home, they should be prayed fully without shortening.