1) Professional writers enjoy writing.
Ha ha, ha ha ha. The best writers I know find the process fairly painful. I suspect this stems from an unhealthy perfectionism borne of the academic culture of worship for great writers. Anyway, some of us say we hate writing, we just enjoy having written.
2) Writers are great spellers and grammarians.
Double ha ha, ha ha ha. I have two dictionaries at work and use them both quite frequently, and ask my copyediting team all sorts of questions about the fine points of English grammar. And I still make mistakes (as any regular reader of this blog will already know).
It’s possible that the sickness that drives one into a writing profession is that you enjoy looking up words, discussing etymologies, et cetera. I have a file of words that I just find interesting. They’re not all obscure. Hairball, melange, lachrymose, whipsaw, paludal, famulus. Many of them are those types of words that provide a window into some other culture. — None of which means I can spell.