Am I understaning the effect of imped. matching?

1. True.
2. True. A few difficult-to-drive speakers can even dip to 1 or 2 ohms.
3. False. I'm not sure that you are properly distinguishing the load impedance that the amplifier's maximum output power is rated at from the amplifier's own output impedance. The output power rating of an amplifier is specified into an 8 ohm resistive load (intended to be a rough approximation of a typical speaker impedance) based on FTC-mandated requirements that are intended to assure consistency in claimed power ratings. But that 8 ohms is not the same thing as the amplifier's own output impedance, which ideally will be very close to zero (and will almost always be less than 1 ohm).
4. True, ideally, unless accomplishing that would compromise other aspects of the speaker design.
5. False. See explanation of no. 3. All amps must be rated into 8 ohm loads. Different amps with similar power ratings into 8 ohms will differ in how well they handle lower load impedances. Several factors contribute to those differences, including output current capability, and the amplifier's own output impedance (as distinguished from the load impedance that it's rated output power is defined at).
6. Assuming you don't overdrive the speaker with too much power, I would put it that the main risk is that the amp can't handle the demands of the speaker load without adverse sonic effects. "Stress" to me implies something that could damage the amp, which is unlikely under typical conditions.
7. It's hard to say, because the frequency or frequencies at which it may be driven out of its comfort zone would be dependent on the impedance vs. frequency characteristics of the speaker. Also, "running much hotter" would result primarily from having to put out high average power levels, which would in turn be mainly a function of speaker efficiency (sound power out vs. electrical power in), which is not directly related to the impedance questions we are discussing.

Basically, some speakers have easy-to-drive load impedance characteristics, and some don't. Try to get an idea of that from reviews, user comments, and impedance vs. frequency curves if available. If the speaker has characteristics that make it difficult to drive, usually high amplifier output current capability and low amplifier output impedance (or equivalently, high "damping factor," which is output impedance divided into 8 ohms) assume increased importance in amplifier selection.

Regards,
-- Al

You got some of it right. There are 2 design approaches, and your ideas are combining both of them which is not a good idea (costs lots of $$$ down the drain).

Take a look at http://www.atma-sphere.com/papers/paradigm_paper2.html

Anytime that devices from the two paradigms are combined, it will result in a tonality problem- too much highs, not enough highs, too much bass, not enough bass, etc. You need to stick to one paradigm or the other. IMO the Voltage paradigm is used to get good specs on paper, the Power Paradigm is intended to match the Rules of Human Hearing with no regard for bench tests (which these days uses the Voltage paradigm rules).

You would think that the bench tests would be testing for the things that are important to the human ear but this is most certainly not the case!

In no. 6, where I said "Assuming you don't overdrive the speaker with too much power ...," I should have said "Assuming you don't overdrive the speaker with too much power, or feed the speaker a clipped, highly distorted waveform that can result from using an underpowered amp ..."

-- Al

Thanks Almarg for hitting most of the key points accurately I would say.