1. Your job as a parent is to educate them with mature and thoughtful responses to everything that they could experience in the world, say, by the age of 16. At this point your job is over, and you don't keep them safe, they go off and explore. I hope we can agree on that. 2. If that is the goal by age of 16, consider working back on the amount of Independence that gets to that goal. And, what are the key measurable goals when you can check off mentally and say 'this kid is on their way to being an independent adult', at different ages? 3. I would work to foster the idea that the internet is not a toy. You go there with a specific task, you get done what you want to get done, and you walk away. You don't get out the table saw and just fool with it. 4. The way to teach a task oriented approach is to do tasks with your kid on the internet. Side by side. Just like you would teach driving or using a table saw... Or in the case of my neice today, grilling. Questions will come up, mistakes will be made, triumph will happen, and you will do it together. 5. I don't see how kids should have email addresses or open screen time before the age of about 12, when you have seen a level of information maturity and critical thinking. The internet is so wild and wooly, i might ask when you allow a kid to fly airlines by themselves, or take a day in the local city by themselves, is about when they should have open internet time.

I suppose I rankle at the problem statement, keep them safe, instead of 'how do we teach independent thought and action', but i tried to answer your question helpfully and positively.