Is it permissible for those who frequent the mosque to engage in worldly matters inside it, and what is the proper conduct that befits its sanctity from them?

It is permissible to converse in the mosque about permissible matters, even if they involve laughter, as long as they are not forbidden or cause disturbance to those praying. It is better to fill the mosques with the remembrance of Allah, prayer, recitation of the Quran, and seeking knowledge.