Regarding your second problem, it seems to me your text messages are stored on the SIM rather than in the phone memory or your SD card. If you use the standard Messaging app, go to Settings, choose Text Message(SMS) (BTW, hey @anon90052001, there’s a blank missing both for SMS and MMS 
), choose SMS storage location - and set it to Phone.
Regarding your first problem: several people have complained about behaviour like that on the forum. In some cases, we seem to conclude that there is a problem with the proximity detection. If the display does not turn off, it stays sensitive for touches, and you might hang up using your ear.
I don’t remember if there is a proximity sensor test in the factory test mode, but probably someone else can quickly comment on that.
There are several ideas why the proximity sensor could be malfunctioning - I have even once speculated in on thread that people with long hair or a beard might not trigger the proximity sensor. 
But it all remains guesswork. I would suggest to try to eliminate potential problems, one by one.
First, try to see if the display is turning on/still on when on the phone. (I suggest a mirror, because it’s supposed to turn on when you move it away from your ear.) Also, try a headset and see if the trouble persists.
You then can try to turn of the display, manually, I think - by pressing the power button after taking/making a call.
If the touch screen is identified as the problem, try to remove factors which could contribute to the problem, One by one. Any phone case, jewellery, headbands, hats… Dunnowhatelse, but be creative. Still guesswork, but better to try that out than quickly contacting support and possibly sending your phone away for technical inspection, right?
