Should a latecomer recite aloud if someone joins him in the rak'ah he is making up, whether it be for the Maghrib or 'Isha prayer? And what are the books that discuss the rulings of prayer related to audible and silent recitation and emergency situations?

This issue is a branch of the disagreement regarding what a latecomer (maṣbūq) perceives with the Imam: is it the beginning of his prayer or its end?

Whoever says it is the end of his prayer recommends that he recite aloud (jahr) in what he makes up. Whoever says it is the beginning of his prayer does not recommend that he recite aloud, and this is the more correct (rājiḥ) view.

The more correct view is that what the congregant (ma’mūm) catches with his Imam is the beginning of his prayer. Therefore, it is not recommended to recite aloud in the scenario mentioned.

Al-Shawkani clarified that the words "فأتموا" (so complete) and "فاقضوا" (so make up) do not differ in meaning here, and that what the congregant catches with the Imam is the beginning of his prayer, as evidenced by the obligation of the tashahhud at the end of the prayer. Thus, it is not recommended to recite aloud in the other two rak'ahs.