If I send someone a letter to remind her of her appointment - can I say "I send a reminder letter to her"
Is it something you do on a recurring basis? If so, then yes. Every quarter, I send her a reminder letter about her upcoming appointment.
if you did it once in the past, then use "sent."
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.