To say that your friend is writing, you would use "Está escribiendo."
Here's a brief breakdown of the options:
- Están escribiendo: They are writing (plural).
- Estoy escribiendo: I am writing.
- Está escribiendo: He/She is writing (singular).
- Están escribiendo: They are writing (plural, repeated).
Since you want to say your friend (singular), the correct choice is "Está escribiendo."