Is the questioner and his mother rewarded for remembering Allah upon receiving the news of the mother's death, even if the remembrance was not specifically "Alhamdulillah (Praise be to Allah)" or "Inna Lillahi wa inna ilayhi raji'un (Indeed we belong to Allah, and indeed to Him we will return)," and without wailing loudly or striking the cheeks?

A believing woman must show patience and seek recompense from Allah when afflicted by a calamity, and utter words that please Allah, such as praise (Al-Hamd) and seeking refuge in Him (Al-Istirja'). She should not cry loudly, as that demonstrates submission to Allah's will. This leads to blessings (salawat) from Allah, mercy, and guidance, as stated by the Almighty: "And give good tidings to the patient, Who, when disaster strikes them, say, 'Indeed we belong to Allah, and indeed to Him we will return.' Those are the ones upon whom are blessings from their Lord and mercy. And it is those who are the [rightly] guided." Allah has also promised Paradise to the believer who seeks recompense from Him upon losing a loved one. As for the reward for your patience, it will not reach your mother unless you intend to dedicate it to her. The deceased benefits from supplication and ongoing charity (Sadaqah Jariyah).