The few KB taken just after midnight is easy to explain.
Your phone uses data all the time, bits here and there, it's not a lot but it happens. If you are connected to a wifi router, your phone will use that by default, but otherwise it will use your mobile data.
The only way to stop this is to turn mobile data off.
Any mobile data that you use in any given day is rolled up into one total that's added to your account at some time after midnight.
Data gets used even when your phone is in standby Some phones will disable wifi after a short time in standby just to save battery. If mobile data is on, they will use that instead, otherwise they will tend to just wait 'til there's a data connection.
This all means you can have data taken off your allowance a) even if you aren't using the internet yourself and b) even when you think it should be coming from somewhere other than your limited and/or chargeable mobile data.
When you exceed your data allowance, any usage of the internet is charged at £1 per day. This includes the background data your phone uses by itself.
You need to establish if you did use up your 2GB and if not, you need to ring 789 to sort it out.