How to limit carrier data usage on iphone 5?

I have an iphone 5 with a prepaid sim, usually used wifi on my old phone but can't seem to tell if the iphone is connecting to the internet by wifi or my carrier network (Which would cost a lot)

Will it always use wifi if it's available or could it be using the network when I'm at home?

Is there any settings to change so that it will limit the data usage on the network, or just warn me when it's going to use the network?

I don't know if its possible to restrict data usage on iPhone 5. But you can always turn off Cellular Data manually. Just go to Settings > General > Network > Cellular Data and turn it off. Turn it on only when you need it. Automatic mail fetching, Facebook feeds, Twitter feeds, weather updates and other background stuffs that use the internet will add charge on your data plan with out you knowing it.

Using smaller browsers like Opera Mini instead of Safari will save huge amount of data when you are on cellular data.

You can set a threshold on android phones based on you limit and you cycle that are using jellybean or newer or use a third party app which is free called onavo count. Onavo count on iphone doesn't do it for some reason though.