Question: If one misses a fard salat when one is a safari (traveler), how many rak'ats must one offer to make it up when one is a muqim (resident)?
If one misses the fard salat of Salat az-Zuhr, Salat al-Asr, or Salat al-Isha when one is a traveler, one must make it up as two rak'ats when one is a resident. There is no reduction in the number of rak'ats of Salat al-Fajr, Salat al-Maghrib, and Salat al-Witr.
Question: If one misses Salat al-Witr when one is a traveler, is it wajib to make it up?
Yes, it is wajib.
Question: If one does not know how many salats one missed while one was a traveler, can one make them up without shortening them?
As one does not do so on purpose, it is permissible to perform them without shortening them.
Question: Is it permissible to perform two rak'ats by making such an intention, "I intend to perform the earliest Salat az-Zuhr that I missed on my journey"?
Yes, it is permissible.
Question: If one misses a four-rak'at salat while one is a muqim, must one make it up as four rak'ats while one is a traveler?
Yes, one must make it up as four rak'ats. However, there is no reduction in the number of rak'ats of Salat al-Fajr, Salat al-Maghrib, and Salat al-Witr.