I would assume that in this instance the Tattoos would take effect in a manner similar to how equipment takes effect on a creature being polymorphed.
From the Transmutation spell description from the Pathfinder SRD:
When you cast a polymorph spell that changes you into a creature of the animal, dragon, elemental, magical beast, plant, or vermin type, all of your gear melds into your body. Items that provide constant bonuses and do not need to be activated continue to function while melded in this way (with the exception of armor and shield bonuses, which cease to function). Items that require activation cannot be used while you maintain that form.
While in such a form, you cannot cast any spells that require material components (unless you have the Eschew Materials or Natural Spell feat), and can only cast spells with somatic or verbal components if the form you choose has the capability to make such movements or speak, such as a dragon.
Other polymorph spells might be subject to this restriction as well, if they change you into a form that is unlike your original form (subject to GM discretion). If your new form does not cause your equipment to meld into your form, the equipment resizes to match your new size.
Essentially this means that if your tattoos require activation, they cannot be used while you maintain an alternate form if that ability or spell changes you into an animal, dragon, elemental, magical beast, plant, or vermin.
However, Since Change Shape (Su) that Kitsune has mimics an Alter self spell, the type that the Kitsune transforms into is always restricted to a specific type, humanoid. Meaning that since the form the kitsune is changing into is of the same subtype ( Humanoid ) all of your equipment ( including tattoos ) will transfer over to the new form.
As far as the first question is concerned, the tattoos will carry over to the original form, yes.
When they shapechange back into their true form and then back again I believe in this instance the tattoo would remain as well, Change Shape (Su) says that the Kitsune can take the shape of "a specific single human form of the same sex". A tattoo is still a "possession" in the instance of it being a magical item that provides an effect.