all (someone) does is (an action)

This phrase is used to show that a person only does one thing. It also expresses that you think they should be doing something else instead:

All she does is play video games.

All he does is work!

sit around

This means to do things that seem lazy or inactive. Watching TV, using the Internet, eating snacks, talking on the telephone to friends are all activities that can be done while "sitting around".

(do something) on the Internet

We use the word "on" to describe using the Internet or using a computer. You can think of it as similar to a train or bus, where you get on and off. If you are using a computer and someone in your family wants you to stop, they might ask:

Can you get off the computer please?

"The Internet" is always "the". You never call it "an Internet" or "Internet".