Text messages are independent of any data transfer, they work from your sim, not internet. Smartphones need some internet time so they can refresh, update etc.. In any case, try taking out the sim and gently cleaning the Gold contacts (I use ispropyl alcohol wipes, the kind nurses use before the give you an injection). Polish them gently and without touching the Gold bits, put it back in. You can get apps that guard your privacy, I don't think Lollipop has the permissions settings, that started with marshmallow.. I have a good firewall that blocks any app from internet as well.
10-15-2016 09:33 PM