Is it permissible for travelers to shorten and combine prayers (Dhuhr and Asr, and Maghrib and Isha), knowing that they will be residing at their workplace for four months, and is Friday prayer obligatory for them in their city of work?

The majority of scholars hold that if a traveler stays in a town for less than four days, he is permitted to avail himself of the concessions of travel. Anything beyond that makes him a resident, and he is not allowed to take the concessions of shortening or combining prayers. The distance that permits shortening prayers is approximately 83 km. Some scholars, including Ibn Taymiyyah, are of the opinion that the travel that permits concessions is what is conventionally considered travel.

Therefore, if you stay in a town for four days or more, you are not permitted to avail yourselves of the concessions of travel (shortening and combining prayers). And if you leave that town for another town that is not separated by a distance that permits shortening prayers, then concessions are also not permitted.

Combining prayers is permissible where shortening prayers is permissible, and in other situations that permit combining.

The majority of scholars hold that Friday prayer is not obligatory for the traveler, and it is recommended to attend it if possible. If the description of "traveler" does not apply to you, and Friday prayer is not established in your town or its establishment is difficult due to the unavailability of its conditions, then it is not obligatory for you, and offering Dhuhr prayer is sufficient. It is not obligatory to go to a town where Friday prayer is established.

As for congregational prayer, one should be diligent about it whether one is traveling or not, and many scholars consider it obligatory for the traveler.