As the topic asks, what could an aquatic civilization use to write on/with?
By aquatic, I mean they live in the oceans, breathe water, etc. -- like mermaids and such. And they are trying to create a way to write in that underwater environment, rather than having a gas pressure dome of any sort.
Edit - additional curiosity: Would tattooing onto skins work?
Quipu is an option. This was the Andean "writing" system, which consisted of colored string with coded knot patterns. Supposedly Hawaiians and Chinese also experimented with similar schemes. That ought to work just fine underwater.
It was pointed out in the comments that this would require access to some kind of fiber with which to make string that would hold up underwater. I believe this is likely to be a given though, as any society without access to that would also not be able to make clothes, nets (eg: fishing nets), ropes, or any other kind of cordage. There are semi-aquatic plants (eg: reeds) that have been historically used for this purpose, as well as animal sinew.
Cuneiform impressions on hydraulic cement using a fish-bone stylus.
The cement is made by mining (on the continental shelf) portlandite and keeping it inside a waterproof membrane. Heat is then applied to the portlandite to dissociate it into calcium hydroxide solution. Steam bubbles inside the membrane are allowed to escape until the contents become a thick slurry of slaked lime. Then you have a couple hours to write on it before it cools down.
This concept is the same as movable type, but instead of using the type to print onto paper, the type becomes the text. Useful for temporary writings.
Use blocks like the Harrapan civilization script with symbols inscribed on them. Then you can string the symbols together to form words, as in Chinese, or ancient Egyptian. The symbols inscribed on blocks would be attached to some sort of board to be sent to someone else to read. That other person could then recycle the symbols when he wanted to write a new letter.
Writing is nothing more than forming characters on a substance. Ink pens work above the water because the ink can dry; not something that's possible in the deep blue sea. However, there is another writing implement that works just as well in the water as out: pencils.
Carved rocks are no different above the water than below it; get something sharp and get carving. It takes a while, but it works just fine.
Pencils, or indeed any soluble substance that can be smeared on another surface (like clay or lead) will work just fine. Writing surfaces will likely be flat rocks, shells, or bones - anything with a broad, rough surface.
Printing is a little more difficult; water-soluble ink is simple to make, store, and distribute. Instead, the mer-creatures will need to invent either a non-water-based ink; oil-based is likely the easiest. Once you have an ink, the rest is easy. And, once you have an oil-based ink, you can make ball-point pens.
On the back of a flat fish whose skin changes color in response to pressure. Then just shake the fish to reset the skin. A living chalk board.
You haven't stated how technologically advanced your civilization is, but assuming they're similar to present-day Earth, you have several options available:
Some of these might require some extra waterproofing to work underwater, but the concepts should work fine.
Carving into stone like many ancient civilizations would still work. Additionally they could make paper like printings using a needlepoint type procedure to embroider text into thin fabric.
Bones, sticks, and rocks tied together like a Marshall Islands stick chart.
Perhaps more sticks and fewer rocks to deliberately make it float, or more rocks and fewer sticks to make it sink, or perhaps just enough to make it neutrally balanced.
The bones and sticks (and possibly, with much more effort, the rocks) could be notched like ogham inscriptions or tally sticks or perhaps carved like Ammassalik wooden maps or oracle bones.
You could think about approaching it like braille? Have a tablet with lots of buttons arranged like a checkered sheet of paper. Each dot/square can be pushed in to form a letter or word and the sheet can be easily reset by pushing all the buttons back out again.
They could have a tool specifically designed for the purpose of pushing these buttons, with each finger (or whatever they have) controlling one of the mechanisms in the tool, which push in the buttons. Obviously this works best with a language that does not have a tonne of different letters
I actually really like the tattooing onto skin idea, or even precision scarring.
For instance, the civilization could have a low/slave caste that basically only exist as slates to write on.
Or slightly friendlier an order of scribes that offer their bodies to preserve history and technology.
On death the skin could be removed and cured (Not sure what the process would be to preserve it underwater), then rolled as scrolls or bound into books.
If they don't want to use their own people, maybe use the skin of aquatic mammals like dolphins or seals.
I have been pondering your question and finally came up with a way to make fabric and thread: http://marinelife.about.com/od/glossary/g/byssalthread.htm
This stuff is made from the fibers mussels use to attach to things. There would have to be an abundance of them in order to make as much as would be needed for writing.
All of the other stuff, like seaweed, or leather, can't really be cured properly enough to do that.
The other way that writing would most commonly happen would have to be via carving--using rock and coral.
As to printing, that's far more difficult to do underwater and would have to be developed gradually. I would think a hydraulic press making impressions in stone would be helpful (if, indeed something like that could even work outside the water.
Burning, either by chemical means or by naturally occurring geothermal heat sources would be a reliable method of writing.
This would probably take the form of "branding" the writing surface (like cattle branding), maybe with a heated metal stylus.
The act of burning a writing surface also opens up a wide array of writing surface mediums that can conveniently be used.
Fisher Space Pens work underwater--there's your pen. Obviously, that's only an answer for a technological civilization, though, they will have to have used something else first.
Provided they have access to some rudimentary form of chisel (a particularly hard piece of igneous rock would work, found near an underwater volcano) they could simply chisel characters into stone underwater.
They could punch shapes into kelp, holding it up to the surface if needed to get light to shine through, or back lighting it while "indoors". The shapes could be based off of a simpler shape like how cuneiform is made from the styled triangles or braille from dots. Longer lasting records just need a hardier material, and permanent ones can use the same writing system carved onto rocks just like on land.
As for your bonus questions - I can't comment on if ink tattooing would work, but there are many other forms of body art that have been around for thousands of years. Scarification always interested me and can often be as complex as tattoos
