Is it permissible to combine and shorten the Friday and Asr prayers, deferring them until after the time for the Asr prayer but before its expiry, in the event of negligence in estimating the time for the Friday prayer? And is the presence of a mirror in the bedroom forbidden or prohibited?

Traveling on Friday is permissible before Fajr by consensus, and not permissible after Zawwal (declining of the sun from its zenith). As for traveling between Fajr and Zawwal, the majority hold it permissible, but it is more cautious to avoid it to exit the difference of opinion. If you depart for travel before the Jumu'ah prayer, you are not obligated to attend it. Instead, you pray Dhuhr shortened, and you are allowed to combine it with Asr, either by presenting (Jam' Taqdeem) or delaying (Jam' Ta'kheer). The preferred method for combining prayers for a traveler who has stopped is Jam' Taqdeem, and for a traveler who is moving, it is Jam' Ta'kheer. Regarding the second question, placing mirrors in homes and rooms is permissible and there is no prohibition against it.