Electrical – Is an LED light strip safe to use under a bed

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.

Yes, you can use a 40w transformer to power your 37.5w load. However, given the quality of these small power supplies, running at 90%+ all the time will cause heat and premature failure probably.

You will need to drive the LEDs at 12v. Running them at 15-18v (or anything over 12!) is a bad idea for the life of the LED. You will need to put a resistor on an 18v supply to bring it down. I'd recommend simply getting the 150w 12v supply. Wattage/amperage is different than volts, where you can use a higher powered power supply and the connected lights will only draw what they need (example: running a 12v 50w light bulb from a 12v power supply rated at 150w is fine. Running a 6v 50w bulb on the same power supply is not fine).