Translation:I want to write.
Again... shouldn't this be "γράψω"?
Yes, it can be! Added as alternative :)
I wrote 'I want to be writing' and it marked this as wrong, but surely γράφω is the continuous form.
Modern Greek got rid of the infinitive.
It did, but Glossmad's answer is in fact correct. Besides, there is no indication of a Greek infinitive in their answer. ;)