How authentic is the Hadith which states that angels forbid a worshiper from speaking in the mosque before prayer, and what is the ruling on speaking about worldly matters in the mosque before or after prayer, especially between the Adhan and the Iqamah?

No chain of transmission (sanad) has been found for this hadith, and it contradicts authentic hadiths that permit speaking in the mosque, such as the hadith of Jabir narrated by Muslim. Therefore, it is not permissible to attribute this hadith to the Prophet, peace and blessings be upon him, and it is not found in the well-known Musnads and books. So, if you see a hadith that contradicts reason, or goes against transmitted texts, or opposes fundamental principles, then know that it is fabricated. Speaking loudly in the mosque is disliked if it causes disturbance to those praying, and it may even reach the point of prohibition. This is supported by the hadith narrated by Muslim from the Prophet, peace and blessings be upon him: "Let those of you who are mature and discerning stand close to me... and beware of the clamor of the marketplaces." It is obligatory to be cautious about using the mosque for purposes other than that for which it was built, as it was built for remembrance (dhikr), prayer (salat), and recitation of the Qur'an.