What is the ruling on smiling—a slight, silent laugh to oneself—during prayer, whether as an Imam or a follower, and what is the ruling on the prayer of those following an Imam who smiles?

Smiling in prayer does not invalidate it unless it reaches the level of audible laughter, as stated by the scholars. Al-Akhdari Al-Maliki said: "And there is nothing upon him for smiling." So, prayer is not invalidated merely by smiling. However, a Muslim should empty his heart for prayer and not think of anything else, and seek Allah's help in doing so. As long as the prayer is valid, there is no need to repeat it or discuss it with the congregants.