Which takes precedence: interrupting the recitation of the Qur’an upon one’s mother calling or upon hearing the call to prayer (adhan)? And is it permissible to not recite with tartil, but rather suffice with silent recitation in one’s heart?

If the recitation is outside of prayer, then it is obligatory to answer the mother, because obeying her is obligatory while recitation is supererogatory. However, if you are in prayer, you should shorten it and then answer her, unless she is seeking help, in which case you must interrupt the prayer to assist her. It is permissible to interrupt recitation to repeat the Adhan (call to prayer) and the remembrance (dhikr) after it. There is no difference in ruling between loud and silent recitation. However, reciting only with the heart without moving the tongue is not considered recitation.