Question: I went to Ankara from Istanbul to stay there for 10 days. I started the fard salat of Salat az-Zuhr to offer it as two rak'ats. While offering the first rak'at, I intended to stay there for 20 days and, therefore, performed that salat as four rak'ats. Did it render my salat makruh?
No, it did not render your salat makruh because you became a muqim (resident) the moment you made that intention. If you had performed it as two rak'ats, your salat would not have been valid.
Question: I went to Ankara from Istanbul to stay there for 20 days. I started to perform the fard salat of Salat az-Zuhr as four rak'ats. When I was offering the first rak'at of it, my friend came and said, "We will return to Istanbul immediately after salat." Therefore, I performed it as two rak'ats. Was my salat valid?
Yes, it was valid because you became a safari (traveler) at that moment. If you had stayed for 15 days there and thus had become a muqim, you would not have become a safari before departing from Ankara.
Question: I traveled from Ankara to Fatih (which is at a safar distance) to stay there for 3 days. I performed Salat az-Zuhr and Salat al-Asr as two rak'ats. I married in Fatih and consummated my marriage there at night. While performing Salat al-Isha, I remembered that my watan al-asli changed to Fatih when I consummated my marriage, so I performed Salat al-Isha as four rak'ats. Is there anything wrong with it?
Your performing it as four rak'ats was correct because Fatih became your watan al-asli. You will be a muqim there until you adopt a new watan al-asli.
Question: Suppose that one is traveling in a northerly direction from the city of A to the city of B (that is at a distance of 452 km). While performing Salat az-Zuhr as two rak'ats in the city of C (that is at a distance of 222 km) on one's way, one stands up for the third rak'at forgetfully. How many rak'ats should one offer if one decides to stay for a month in the city of C before or after performing the sajda of the third rak'at?
If, before doing the sajda of the third rakat, one intends to stay for more than 15 days in that city, one will have to perform that fard salat as four rakats. But it will be necessary for one to repeat the qiyam (standing) and the ruku (bowing) of the third rakat because one has performed those two (the qiyam and the ruku) as parts of a nafila (voluntary) salat. (Se'adet-i Ebediyye)
If one decides to be a muqim after the sajda of the third rak'at, one must perform one more rak'at and make them four. However, this salat has turned into a nafila salat. For this reason, one must repeat Salat az-Zuhr.