Does staying up late become forbidden for one who misses Fajr prayer due to it a few times, and is a person's going to the market after 'Isha' or delaying their sleep for studying or conversing with siblings, while being careful to return before midnight, considered forbidden if that does not usually lead to missing prayer?

Staying up late is not forbidden; however, it is disliked to converse after 'Isha' prayer unless there is a strong benefit, such as hosting a guest or seeking knowledge. Otherwise, it is preferable to sleep after 'Isha' to wake up actively for the night prayer (Qiyam al-Layl) and Fajr prayer. Al-Bahuti cited the hadith of Abu Barzah al-Aslami, which dislikes sleeping before 'Isha' and conversing after it, but exempted conversing about Muslim affairs, for work, with family, or with a guest. Sleeping before the prayer time does not make one sinful if they miss the prayer, and what is prescribed is to take measures to wake up and pray immediately upon waking. As for after the prayer time has begun, it is forbidden for someone to sleep if they strongly believe they will not wake up before the time expires.