Brazier mechanics have recently changed, so information on the page is not complete.
Brazier damage is thought to have a base of ? Black Bile per shot, with modifiers that increase and/or randomize it; This damage is reduced when within the range of other Blazing Braziers. Individual braziers do considerably less damage but will critical hit far more often.
Take note that you do not need to "light" a blazing brazier, it will automatically ignite when it detects a crime near it, as long as it has coal. Crimes of vandalism immediately awaken braziers (and Torchposts). Light duration, when activated, stays on for exactly 5 minutes after a crime then turns off. Uses far less than 1 piece of coal. The effective range was confirmed by devs to be 120 pixels, which makes 11 tiles (11 pixels per tile).
To destroy a brazier you first need to use a full bucket of water on it. Then wait until it is destroyed by decay. To repair the damage done by the water you only need 1 Bar of Pig Iron;
Braziers have purity which can be increased by Unscathed Wood even if the brazier is full.