What is the ruling on speaking loudly about worldly matters in the mosque between theadhan and the iqama and after the prayer, and what is the ruling on sending children back from the first row to advance to it?

Speaking about worldly matters in the mosque is permissible and entails no sin. However, it is contrary to what is most virtuous. The Prophet (peace be upon him) approved of the Companions doing so, provided that the speaker does not disturb any of the worshippers by raising their voice. As for how to deal with those who are speaking, it is advisable to be gentle and lenient, explaining the Sunnah with wisdom and good admonition, while striving to maintain unity and solidarity.