As I don't know the interns of this dimmer it might switch when the alternating voltage (and therefore the current with resistive loads) crosses zero. To detect the phase (crossing 0V will occur at 0° 180° and 360° which is again 0° - you might want to look it up here: http://en.wikipedia.org/wiki/Phase_(waves) ) and the type of load (e.g. inductive loads delay the flow of current depending on their inductance and the frequency in relation to the voltage. I could not find a text on wikipedia describing that so here's a plain image: http://people.sinclair.edu/nickreeder/eet155/PageArt/phaseInductor.gif
To detect the type of load it has to observe the mains line for a short period of time without regulating it.
The issue does not occur on light loads because most dimmers can handle inductive, capacitive and resistive loads quite well on low power levels.
By letting the dimmer "cool down" you may erase its short term memory so it has to resynchronize every time you switch it on.
Again: As the internals of this dimmer (or better: the two) are not known I can't provide a better answer. A newer hardware revision usually improves the product. Also chinese manufacturers tend to produce lower quality products as seen here: http://hackaday.com/2012/08/15/buying-cheaper-electronics-and-not-saving-money/
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.
Best Answer
You will need a ohmmeter. Disconnect the IR Controller (the white box with white wires). If you check the the voltage drop (in the connector of the white wire) between the Positive (+) and the different wires. If you find that they all respond to commands from the remote... except for the port for the blue wire (which controls the blue light), then the problem might be with the remote or the receiver. Again, if the "blue port" always reads 12VDC (despite trying to turn it off), then the problem is with either the remote or the receiver (and not the strip).
However if it does turn on and off upon command, then there must be a short in the strip or connectors (powering the blue wires).
If you look carefully along the strip you might be able to see where the short is (often looks like a burned/discolored spot (or a discolored LED). If you bought the non-waterproof strip, then you might find some debris or dried soda or something on the strip. Or if you have the waterproof strip, you might see a crack in it where humidity has collected and is causing a short between + and B.
If everything seems to be looking okay, then you could get some short pieces of wire (strip the insulation off of both ends) and insert them into the connector- making sure to only connect one wire to each port- and perhaps diagnose which wire is connected to the Blue lights by connecting one wire at a time... then two wires at a time... and (if necessary) three wire combos. Unfortunately, this may not be a fruitful piece of information, because it seems that the problem is with the strip or one of the LEDs anyway, and if you don't see any obvious faults then there's not much you can do figure out where the issue is on the strip.
So of course, if you have no idea where the fault lies (just on the strip somewhere) you'll have to cut out the bad section by cutting the strip in half. One half of the strip should be okay... then you cut the bad half in half... and just walk-it-down until you're satisfied. Then you can reconnect some of the lengths worth keeping.