Question: 1. The time children spend (or spends) watching TV.
2. The time children spend (or spends) working prevent (or prevents) then from focusing on their school work.

Could you please help on the above sentence corrections. And the explanation as well.

Answer: 
It's used to more clearly differentiate between the two meanings of writing for a magazine. It can be both the physical act of writing (pen on paper, on a computer etc.) or it can also mean the act of being employed by the magazine submitting articles sometimes. 

By writing it this way, it's shown that we're talking about her being employed by the magazine, and not that she is writing physically while jack is talking. (presumably taking notes about jacks story)
One of the uses of the past simple is to indicate activities that the person habitually engaged in. The past continuous is used to indicate an activity that the person was, at that time, engaged in. So by using the simple past, the writer is indicating that she habitually wrote articles, not that she necessarily was at that moment writing. The past perfect is used to indicate an action that is completed. Since the writer wants to discuss ongoing conduct, the past perfect is not appropriate.