Is what happens to the questioner—forgetting what he has read or heard after a period, despite its being firmly established in his mind and his application of it, along with his inability to recall it when trying to teach it to someone else—a normal matter, or is he suffering from memory impairment?

The purpose of knowledge is to act upon the sacred texts. There is no blame on a Muslim if he forgets their exact wordings, as long as their meanings have settled firmly in his heart. This is what scholars have affirmed regarding Tawhid (definition) (monotheism) and all other religious obligations. As for memorizing the details of the Sharia (definition), it is a collective obligation (fard kifayah) for those who undertake the task of conveying the message. What the questioner experiences, namely forgetting the exact wordings after hearing or reading, is natural due to the abundance of distractions and the accumulation of information. The way to firm up knowledge is through memorization, repetition, and revision.