Iphone data running out at home?

[IBeBrad]

I am looking to change my contract/sim to another network such as 02 as I am currently on orange
Over the last few months I have been running out of data and going over my contract.
I assumed if you are connected to your internet rooter at home then your data isn't charged unless you are outside using wifi?
I am nearly always at home and use my phone at home to go online and things but Sometimes it says 'no service' alot and I had to ring and get them to sort it out (it took over 45 minutes on the phone!)
and it went back to normal for around 1 week then did the exact same.
I was wondering if thats the reason its been taking my data
I use alot of social apps and games such as facebook, tumblr, instagram, twitter, and games.

Is Oranges rubbish connection the reason for my data loss?