Only contacts approved or added by a parent can contact or be contacted by the child.
Your child can add his/her own contacts by going to Contacts on their monqi phone, clicking the + icon and then going through the process. The new contact will now come to the parent for approval. Only after accepting the contact the child can contact this individual through call or SMS.
The parent can also add contacts to the child's phone. Swipe up on main screen, scroll down to select Contacts. Here you can edit or delete the child's contact, or add new contacts either from scratch or add them from your own phonebook. To add from own phonebook click the small + icon.