Is laughing at someone's mistake while they are reciting the supplication "Allahumma zid wa barik" (O Allah, increase and bless) – due to a letter being changed which made it embarrassing – considered apostasy? And if so, is this apparent to the sisters present despite their not knowing the reason for the laughter?

Laughing out of embarrassment due to a mistake is not mockery of religion or an affirmation of falsehood, nor does it necessitate obsessive worry about apostasy. One should seek refuge in Allah from Satan, cast away such thoughts, and not dwell on them, for obsessive doubt is a severe illness that leads to confusion and pathological skepticism.