If this is happening on more than one device, it rather points either to usage or a rgoue app. Are you accidentally catching the top of the screen and pulling the notification blind down? I sometimes manage to launch Google Now by doing the same thing from the bottom of the screen.
I've never heard of an app doing this, but there's a first time for everything. You could test this by doing a factory reset (don't forget to back up your content first) and then running the phone vanilla, with no additional apps added, for a few days. If it's stable, put your apps back one at a time until the problem recurs and you've found the culprit.
With regard to mobile data, try going into Settings|Mobile Data and seeing if there's a "get settings from provider" option. If there is, tap it and it'll pull the settings down and install them. If not, then the phone thinks you have the correct ones. You could also, in the same section, have a look at Access Point Names and make sure that Vodafone Contract or Vodafone PAYG is there and has a green dot beside it, meaning it's set as the default. if something else has the green dot, long press the correct one and then tap "set as default".
You can also get the settings by texting WEB to 40127.
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