Q: block apps from the internet

Don't use them...uninstall them...turn cellular data off...those are your choices.

iOS: Understanding Restrictions

Do as wjosten said: turn 3G OFF then.

Nope.

iOS: About cellular data usage

You can also temporarily disable cellular data when it’s not needed.

• From the Home screen:
  • iPhone: Tap Settings > General > Network
  • iPad: Tap Settings > Cellular Data
• Slide the toggle next to Cellular Data to off. This will disable all cellular data traffic until it’s enabled again.

These phones are junk, I am so ready for a stinking lawsuit! Im so angry with all the garbage! For that much money, I'd say gougers! You should not have to turn your data on and off all the time. It should block them if you want and still have data access for messaging and such! Garbage. And this is not the only problem! There are several issues with the iPhones and not worth the time, money,  nor effort it takes. If its insured, send it back and have it replaced maybe and keep complaining until they do something about it.

This is a user-to-user technical support forum. No one here really cares what you think of iPhones or Apple. Submit your feedback directly to Apple:

http://www.apple.com/feedback