Can't define APN: "Unfortunatelly, Settings has stopped" - SG 4

I have Samsung Galaxy S4 with Android 4.4.2, Kernel 3.4.0.

After returning from abroad and switching back my SIM card I've noticed, that mobile internet is not working. I've noticed in the Settings, that no APN is defined. When I click '+', there's the error:

Unfortunatelly, Settings has stopped

Restarting the device has not helped. Restarting the device without SIM card and them again with SIM card hasnt' helped (I've noticed, however, the error icon appearing for a second in notifications and them disappearing). Configuration SMS from operator hasn't helped.

I've switched SIM cards many time on that device, and I've never had to configure anything with the internet, it's the first time I get that error, and it seems to be persistent. I suppose some configuration file is broken.

What can I do to fix that? Restoring factory settings would be the last resort, because I have many settings that I'd loose, for example it took me many days to disactivate all Samsung malware that was draining the battery... My phone is not rooted and it's not the option to root it because it's the company's handy.

What can be the reason for such behaviour and are there any solutions I can apply with non-rooted device? For example, deinstalling some system updates, or installing some?