Learn Russian: Я часто напоминаю моему старому дедушке о лекарстве. - I often remind my old grandfather about the medicine.

They are in the Dative case. The verb напоминать (to remind) requires the Dative case for the person receiving the reminder. For masculine words, possessive pronouns like мой take the ending -ему, and adjectives like старый take the ending -ому.

Since 'grandfather' is masculine, why doesn't дедушке get a standard masculine Dative ending?

Even though дедушка is a masculine word and takes masculine adjectives like моему старому, it ends in -а in its base form. Nouns ending in -а follow the same grammar rules as feminine nouns, so the -а changes to -е in the Dative case.

Why is the medicine written as о лекарстве?

The preposition о means 'about' and requires the Prepositional case when expressing the topic of a reminder. The dictionary form of the word is the neuter noun лекарство, and changing the final -о to -е puts it in the Prepositional case.

How do we know to use the imperfective verb напоминаю instead of its perfective pair?