Are they applicable on only one character, or on each and every one you own? And new ones that you create?

Yes. And the cosmetic changers are consumable. If you use one and unequip the modded item, then the NPC will give you another copy of the consumable. (They just didn't want the consumables to stack or be permanent, for whatever reason, except for the permanent Wisp jar)

But a modded item is Soulbound, meaning it cannot be traded or even moved to your shared stash. If an item is good enough to be handed down, think twice before turning it into a snazzy officer's jacket or wig or whatever else.

The mod is best used on temporary gear that's "good enough" but not ideal, or on anything you have an extra copy of.