Is the son obligated to obey his mother who prevents him from going to the mosque for congregational prayers, the Adhan, and the Iqamah, on the pretext of his young age?

It is not permissible to obey your mother in preventing you from praying in the mosque or from performing supererogatory acts. However, understanding your mother's motivations, which are often driven by fear, should make you compassionate towards her and lead you to address her in the best possible manner. You should try to manage her and please her without disobeying Allah. This can be done by obeying her in some supererogatory matters (such as the call to prayer and the iqamah sometimes) to win her heart, as the benefit of winning hearts is greater than the benefit of performing supererogatory acts. Fulfill your religious obligation without letting it turn into a battle with your mother.