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.
Usually you use the two outmost connection points for +/- 12VDC on the strip ... and usually + and - leads are marked by printed labels on the strips at each seperation mark.
For connection from power supply to the strip you either use the premounted socket (if any is mounted at the end of the strip) or you solder the cables coming from the transformer / DC source onto the connection pads.
With the shopping list of your OP I would do the following wiring
+-------------+ +-------------+ +---------.
~| |+ ---------- +| in out |+ ------------ +|
110/220VAC | Mains/12V | 12VDC | Dimmer | 12VDC PWM | Strip ....
~| converter |- ---------- -| |- ------------ -|
+-------------+ +-------------+ +---------.
The power rating of your ACDC converter is a function of the length of LED strip you want to use. If I am not mistaken - a single tripple of LEDs (the smallest separable unit) takes 60mA ... so all 300 LEDs (100 sections) would require as much a 6000 mA (6A)
The current limit of the dimmer is 12A which is fine for the whole strip.
If you are using more than -say- half of the strip I would consider more than 1 feed point to avoid voltage drops along the strip.
Best Answer
Longevity: LED's are generally marketed between 50k-100k hours of burn-time. I installed them throughout my home 18 months ago; none of them have failed yet.
Grime Resistance: For a kitchen, buy waterproof strip lights like these - they'll hold up against steam. You can also fabricate an easy-to-clean cover using clear PVC and brackets
Heat: If the strips are installed correctly, each LED will be cool to the touch. Monitor the installation for excess heat and wire in a resistor if needed.