How does one perform the shortened prayer (salat al-qasr) and combine the Dhuhr and Asr prayers by advancing them, and the Maghrib and Isha prayers by delaying them, for a Muslim residing in a foreign country?

If you travel the legal distance for shortening prayers, it is sunnah for you to shorten the four-rak'ah prayer to two rak'ahs after you leave your place of residence.

If you reach your destination and intend to stay for four days or more, you complete the prayer.

If you do not intend to stay for the aforementioned period, you continue to shorten the prayers until you leave that place, unless you have a wife there or it is your homeland.

It is permissible for you to combine prayers during travel (Dhuhr and Asr, and Maghrib and Isha), either by performing them earlier (taqdim) or delaying them (ta'khir).