Are remote study circles considered to be included in the Prophet's (PBUH) saying: "No people gather in an assembly remembering Allah Almighty, but the angels encompass them," and is supplication in them better? And is the questioner sinful if she is compelled to listen to lectures while doing her housework?

Listening to knowledge via media does not fall under the meaning of "gathering" mentioned in the hadith (definition). Supplication in gatherings of remembrance is among those prayers for which an answer is hoped. It is recommended to listen to knowledge during free time because it is more conducive to attentive listening, comprehension, note-taking, and memorization. The beginning of knowledge is attentive listening, then listening, then memorization, then acting upon it, then dissemination. If listening during work is the only option, then there is no harm, and the Muslim should strive to listen attentively and follow along as much as possible. Attentive listening to the recitation of the Quran is recommended, not obligatory. For knowledge other than the Quran, it is even more appropriate that attentive listening is not obligatory.