Is a water world possible, and for how long could it be stable? I have several questions regarding this topic.
First, could a water world be stable for thousands of years with most of its surface remaining covered in water. What would it take for this to be possible?
Second, in the said world, would it be possible to have an atmosphere stable for human life? By stable, I mean oxygen levels near 20 percent without any harmful toxins. What would this require to be maintained?
Would it be possible for this world to exist with no moon, no tidal forces, and to be locked from rotation? Would there be any sort of tide or waves associated with the water in this condition?
How far from the Sun would it have to be located to be safe for human life, and what might the Sun look like in the sky? Would the Sun's position in the sky remain constant?
I'm sorry for the abundance of questions. I don't know where else to find the answers, though I've read several books on the topic. I've heard of Excel spreadsheets that will help you answer these sort of questions, but I don't know where to find them or how to use them. Any help would be most appreciated!
One final thing: When I say water world, I mean water as we know it (H2O) and not some sort of sulfur ocean or any other such thing.
Have I failed to ask about other in-depth information on this type of planet?
 A: I'm very far from an expert, but it's an interesting question and I have a few thoughts. 
Regarding the first question, "could a water world be stable for thousands of years with most of its surface remaining covered in water", being somewhat pedantic the Earth would meet this description, so yes (and I presume you really mean 'millions' if not 'billions' of years?) - although even then the "Snowball Earth" hypothesis would suggest that this state is not completely stable on those timescales. There is presumably a relatively narrow window of temperatures for stability, as too cold and the water will freeze to ice (e.g. the assorted ice-rich moons of the outer Solar System), while too hot and you'll lack a defined surface as water transitions to vapour. Both would appear to be runaway endpoints, i.e. as the planet heats up, the atmospheric water content increases, which increases the greenhouse effect, which promotes heating, etc.
Gravity might also be problematic, at low mass the atmosphere will be less dense and more easily lost, while at higher gravities the efficacy of water vapour as a greenhouse gas might lead to high temperatures and pressures. Which I guess is some kind of consideration for your second question. 
I don't quite follow the tidal locking question, but this would suggest a reasonably compact orbit which would in turn lead to the temperature runaway and/or loss of atmosphere problem (and literal evaporation if there's no rock core). Maybe with a cool M-dwarf star this might be possible, I don't know.
A quick browse of the arXiv turned up an interesting looking paper from the journal Icarus
http://arxiv.org/abs/astro-ph/0308324
which might give some more insight (from someone who knows what they're talking about ;) but i've not yet had time to give it a read-through - skipping to the conclusions suggests that it is at least possible, if an ice-rich planet subsequently migrates inwards. 
A: In its past, the Earth had conditions where the continents were less active and most of the planet was covered by shallow seas. So, the Earth could have no land, and continue much as it does now provided seas were shallow. Deep oceans, however, tend to be relatively sterile at the top, and without water running over land to supply nutrients, there would be much less photosynthesis to supply the oxygen. Volcanos would still erupt and supply nutrients, and carbon dioxide, however. In summary, I would predict that a water world would have less oxygen and more carbon dioxide than the Earth does now.
The sun would still exert a tidal force, even without the moon present. It is about one-half of what the moon's tidal force, and there is no way of getting around it. If the Earth's rotation were locked with the sun, then the tides would be permanent and unmoving. There would still be ocean current, of course, because of the unequal heating between the equator and the poles.
If the earth was locked to the sun, then the side away from the sun would freeze over, probably to depths of tens of meters, but the current would carry enough heat from the warm side to keep it from freezing more deeply than that.
Without the moon to stabilize, the earth's axial tilt would be unstable over long periods of time, but if you are going to do away with rotation, that shouldn't matter much.
Without rotation, the earth's magnetic field would go away, allowing harmful solar wind particles and cosmic rays to enter the top of the atmosphere, causing a rise in radiation levels. But they shouldn't penetrate the ocean too far.
Without land to freeze or overheat, the habitable zone from the sun may well be larger; at the outer part of the habitable zone, only the part of the earth facing the sun would be ice-free. At the inner part, there would be no ice even on the dark side.
A: Read more on exoplanets. It is believed that planets may exist that are covered by oceans many dozens (or hundreds) of kilometers deep, no dry land at all. Yes, they are stable. What it takes to make them? Lots of water, of course. The exoplanet subtype that fits your description is the Ocean Planet.
http://en.wikipedia.org/wiki/Extrasolar_planet
http://en.wikipedia.org/wiki/Ocean_planet
If the ocean is very deep (hundreds of km) then water at the bottom may exist in strange varieties, such as hot ice (it's hot because it's deep and close to the core, but it's solid due to the humongous pressure). Read about the phase diagram of water.
http://www.lsbu.ac.uk/water/phase.html
Breathable atmosphere? That requires oxygen. That's definitely not stable long-term because it oxidizes rocks and stuff, so it requires the existence of oxygen-producing plants in the ocean.
No moon? Sure, it's possible. There are discussions whether the apparition of life requires a big moon and tides (and some dry land), but this is only speculation at this point. Life may have come from outer space, for all we know.
"Locked from rotation"? You mean, one year is equal to one day? That's kind of not very likely. If it's very close to its sun, then over a very long time, such a world may get tidally locked to its sun, so there would be no sunrise, no sunset, and no "days" as we know them. But this is by no means due to having vast amounts of water - water is irrelevant in this context, any world would do the same, regardless of its composition.
In any case, if it's not tidally locked to its sun, then tidal waves would be just like on Earth in the middle of the Pacific - pretty mild. If it's locked to its sun, there would be no tidal waves.
How far from its sun? Depends on how hot that sun is. Hotter than ours - then it needs to stay further away. Cooler than ours - then closer.
Sounds like you're writing a SciFi book, or something, and you're doing research. :)
