Both reading and writing are necessary, but writing alone is not sufficient.
Yes, but there's a significant asymmetry with the advice usually given. I hear "Read a lot" about 10x more than "Write a lot".
I've been reading a lot for decades. I'm a crappy writer. There is a saturation point.
Any art needs theory, practice, and study of the greats. Unless you're some kind of exceptional genius talent out of the gate - and no one is, really - you need inspiration from other work, imitation, understanding, and practice of your own work.
It helps a lot if you're obsessive and/or enjoy it a lot. Ideally both.
None of these are a substitute for talent, but likewise talent isn't a substitute for them.