Suddenly my Galaxy S4 the messaging slow down and now I have to turn on my data to speed it up.

I was always able to text without having my data or Wi-Fi on, now the phone won't send the text, keep saying sending and it doesn't go through until I turn on the data and it doesn't work over Wi-Fi. Previously I only had to turn the data on in order to receive or send a picture. The cachet and storage is always cleaned, I have deleted all previous texts and history, when under the Builder developer and change settings with the animation options, nothing is working. Tried downloading different apps and still running into the same problem. I'm looking for an app that would work but yet I would have some privacy as the messenger that came installed on the phone gives me absolutely no privacy and has access to everything in my phone.

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.