The damage of the dot itself is actually not affected by any of the weapon‘s modifiers (it is affected by perks).
Only indirectly through max number of stacks.
Burning intensity might be the direct damage of the flame coming out of your hand (edit: it is not. it looks like it is the tick rate of the direct damage from the charged attack).
I think the stats do exactly what they say they do.
You are right about that. I should have looked ingame, before i commented in regard to “burn intensity”.
Since the “burn intensity” value decreases with higher stats, it is probably the tick rate of the direct damage from the secondary attack.
Max dot stacks: how many stacks of the dot effect can be applied to the same target
Dot application rate: rate at which stacks of the dot effect are applied to a target
Secondary action burn intensity: rate at which the direct damage of the secondary attack is applied
Damage caused by each tick of the dot is independent of weapon stats (except bonus damage perks).
Damage tick rate of the dot is independent of weapon stats.