No point in replacing the cotton without cleaning the coil at the same time. I always do both at the same time.
For me, usually vape unflavored. It still tastes fine to me after a week, but the coil begins to look dark. However, when I rewick it and clean the coil, I'm surprised how much 'cleaner' it tastes, even when it didn't look bad.
Personally, I've just gotten in the habit of rewicking/dry burning weekly for unflavored juice, and daily with flavored juices. I'd rather not be heating any of the 'crud' along with my juice. It's not a big deal to clean and rewick regularly to me. Whether or not I can taste a difference before I rewick/clean, I always seem to be able to after.
Whatever you're fine with I guess. You'll definitely taste a difference when it's time. I just prefer to stay on a schedule so I don't have to do it unexpectedly.