1. Let's try with an the verb to sit. If you want to rest your legs, you bend your legs and lower yourself onto some horizontal surface: you sit (simple present). After you come to a rest, as long as you remain in that position and do not reverse the process, you are sitting (present continuous).
2. Perhaps you heard someone saying that and misheard or they said it wrong. You are correct: "Don't call me, I will call you".
Student or Learner