Is using the continues form common? Is it considered more formal? If a Dutch person were to approach someone who is writing, would he use "Schrijf jij?" or this form?
"Ben jij aan het schrijven?". For sure. It's not more formal or anything, but the tense for "Schrijf jij?" sounds a little awkward to the native ear. This tense could very well be compared with "Do you write?". You could use it when you're sitting next to a writing person, but "Are you writing?" would be the more natural way to go. "Schrijf jij?" is more likely to be used when you want to aks if someone is writing in general, like if he is an author or writes books.