What is the ruling on a traveler combining Dhuhr and Asr prayers on a Friday in a mosque where Jumu'ah prayer is not held? And is it permissible to combine the two prayers without shortening them in order to catch two congregations, both of which pray Dhuhr without shortening it?

It is permissible for a traveler to combine Dhuhr and Asr prayers on Friday, and he is not obligated to perform the Friday prayer while on the road. There is no connection between combining and shortening prayers; thus, combining is permissible without shortening and vice versa, and shortening is better than performing the full prayer for a traveler.