She remembers me? What's this mean? Is it like "She often thinks of me"?
помнить - to have memories
вспоминать - to remember
That's how I've seen it explained here, but I'm not sure I get the difference yet.
I understood it the other way around where:
помнить: to remember things, to have a memory;
вспоминать: to recall, reminisce about something in the past.
According to Wiktionary, the prefix вс- is an alternative form of the prefix воз-, the general sense of which is shown here: https://en.wiktionary.org/wiki/%D0%B2%D0%BE%D0%B7-#Russian
I got this correct, but I was wondering if it could also be, "she often reminds me (about something)."?
for that, i think you'd use напоминать...
она часто напоминает мне взять лекарство. = she often reminds me to take my medicine.
мне is dative (the indiкect object) while меня is accusative (the direct object). There are exceptions, where verbs take a case that we would not instinctivelt expect, but as a general rule, the thing acted on by the verb goes into the accusative case.