Why leave out the "er" here? I guess it is the same as "we write"?
Yes, there is only one present tense in Norwegian, so it covers both the simple present and the present continuous in English.
How does one differentiate between continuous action and present action in Norwegian?
Most of the time you will either know by context, or have no need to differentiate.
There are ways to express continuous action in Norwegian as well, which you'll learn in the 'Continuous' skill, but it's done much more sparingly than in English.
there's only one kind of present like a lot of other languages
Is 'skriver' also 'to write' ?