Ellipsis

(a) Both communication systems allow you to send and receive text messages and to ask and answer questions.
(b) Both communication systems allow you to send and to receive text messages and to ask and to answer questions.
© Both communication systems allow you to send and receive text messages and ask and answer questions.

  1) Which sentence(s) above is/are grammatically correct?
  2) Which ones sound natural?

They’re all okay but ranked in order of fluency, I would place them in this order:
(a) 1st choice.
© 2nd choice.
(b) 3rd choice. There’s too much unnecessary repetition.