For the triggered ability to trigger, Warchanter Skald has to actually change from untapped to tapped. If an effect attempts to tap while it is already tapped, the ability won’t trigger.

Warchanter Skald’s triggered ability doesn’t allow you to tap it. You have to find some other way to tap it. You could attack with it, I suppose?

If Warchanter Skald isn’t enchanted or equipped at the moment it becomes tapped, the ability won’t trigger at all. If the ability does trigger, it will check again as it tries to resolve to make sure Warchanter Skald is still enchanted or equipped: if not, the ability won’t do anything. (Warchanter Skald could have different Auras and/or Equipment attached to it by that point, though.)