Do the side conversations that intersperse lessons of knowledge invalidate sessions of remembrance [dhikr], understanding matters of religion, and memorizing the Quran?

There is no religious impediment for students of knowledge to discuss their private matters or to socialize with each other, so long as this does not lead to negligence, wasted time, backbiting, or slander. The Companions used to converse in the mosque, and this was also the practice of the righteous predecessors. Scholars used to narrate stories and anecdotes to alleviate seriousness and monotony.