Not a complete answer, but here's some more info.
Brightness
While there are ways to calculate this that aren't that complicated, it requires knowing many coefficients that are not readily available, so ends up being an educated guess at best. You can do just as well totaling your current lighting's lumen output, then adjusting for changes in fixture styles. (I consider even a simple LED strip a "fixture" for the sake of this discussion) It's a starting point. If you use proper task lighting, there's a lot of room for variance in total levels.
Uneven light
You do not want to see the actual LED elements, it's really annoying. Besides diffusers, indirect lighting techniques work well, though require more lumens due to losses through reflection.
Positioning
I'm not sure what the issue is with parallel surfaces. The efficiency is mostly inherent in the fixture's ability to direct light where it's needed. The mounting surface has little to do with this, you need to direct the light where it's needed.
White Light
The "whiteness" is measured in degrees Kelvin. The temperature a black body must be heated to emit the same color of light. Standard daylight is often taken to be 6500K, anywhere in the 5000-7000 range is close enough for most tasks. You eyes adapt quickly to small variances. In residential settings, daylight is considered too harsh because we are so accustomed to incandescent lighting, so most home lighting is produced to output more in the 2000-3000K range to mimic the orange incandescent lighting.
Noise
How audible the noise is varies by manufacture and environment, as well as personal temperament. I don't think noise data is readily available. Testing in a noisy store will not yield any useful data, other than if you can hear it from a few feet away it is too loud. Noise can be attenuated by placing it in an enclosure, but keep in mind power supplies generate heat that has to be removed by ventilation, you cannot seal it into a sound proof box.
Try to place power supplies as far from your pillow as possible, trying to sleep is when it will be most bothersome. Placing it lower so there is likely to be more furnishings obstructing a direct path will help, as well as being surrounded by soft materials that do not reflect sound as well.
As Dan says, there is a maximum to the number of connected segments you can run. After that, you can get "RGB amplifiers" that are powered, and run the next set of segments.
You should take into consideration:
- The max length of a segment on a single power source (as published by the manufacturer)
- The size of the power supply needed, and the space you have for supplies
- The cost of amplifiers and power supplies
It may make sense to have several small(er) power supplies rather than one or two large ones.
Best Answer
Not sure the level of problem you are taking on here. Most "bare" LED strips you can pick up these days are DC based, and you need to add a AC to DC power supply that provides the voltage (12 or 24v) and current required by your strips. First you need to find those requirements and pick a supply.
Next, you can daisy chain these strips together, soldering low voltage wires from one to the next, to get all the way around your room, though I wouldn't recommend that. The problem is that the copper in the strips is not very thick, and there will be a voltage drop over the length of the strip, so the end LEDs will be dimmer than the first.
A better plan would be to feed them from the center out. A even better plan is to run a separate set of wires from the power supply to each strip. The number of wires will vary depending on if the strips are single color, multi, or RGB.