Ok (not sure how to take that!)
Go grab the stuff you need to measure Z, and go nuts. Let us know how your adventure turns out.
It should be variable. A decade box is a set of resistors and switches that lets you pick a total resistance and read the value on a set of switches. You can also use a pot, set it to the desired value and measure the value with your DMM.
But seriously...you can Google this stuff, man! All the answers are already published, plus answers to questions you haven't even thought of.
You missed some "or"s here and there. A Y splitter, headphones (assuming the impedance of the headphones at the testing frequency is known, which it pretty much is for many common models, at least close enough), and built-in sound card is sufficient. You can use either the sound card or DMM to measure the level, so you can skip using the DMM. Resistor is an alternative to using headphones, so you can skip that as well.
The key is to measure the level when the load is connected and then again when it is not. How much the value changes between the two measurements, with some easy algebra (and knowing which equations to use), tells you the output impedance.
No adjustment. That's a range of suggested impedances for things you can connect to the amp, but these amps should be perfectly happy with more than 600 ohms too. 32-600 ohms just covers most headphones people have, so it's a convenient range to list for advertising purposes.
They're just kind of making a suggestion that you not run stuff under 32 ohms (read: many IEM models, which also happen to be very sensitive) on them. Some headphone models are under 32 ohms, but not many. Some amps start significantly misbehaving when driving lower-impedance headphones and IEMs. Maybe more significantly, they may have relatively high noise floors and may not sound that stellar for using some IEMs. Maybe the amp has a relatively high output impedance.
By that token, some amps are listed up to 300 ohms. These models tend to actually not have enough output power to reach loud listening levels for most 600 ohms headphones (it should sound good, just not loud enough for some people). Again, it's not really a technical limitation as much as advertising and setting expectations.
Anyway, it's not like there's a sharp divide between in the range of 32-600 ohms, or whatever they list, and outside the range.
While we're on the topic, I've heard that mechanical and acoustic damping play a much bigger role in controlling the motion of a dynamic driver as opposed to electrical damping. Can low electrical damping make a good driver perform poorly? Vice versa?
It's very situational. You have to consider the entire system as a whole including mechanical and acoustic factors as well as electrical. No easy answer, but generally you want more damping wherever possible, with the goal being better impulse response and less overshoot.
Generate a 50 Hz sine wave and put it on your portable source. Connect the cable to it, play the file and measure the voltage between tip and sleeve or ring and sleeve.
Do the same the headphone connected. You may need some crocodile clips to connect the two male jacks (tip-tip, ring-ring, sleeve-sleeve).
Headphone splitter here:
Plug to use with your DMM for test access here:
Clip leads to connect your DMM to the test cables here:
Free test tones here:
It is easier and cheaper to make an amp that does not have very low output impedance. Adding an output resistor of 10 to 100 Ω is a simple work-around to several problems (like stability issues with capacitive loads, short circuits, and too much power into low impedance headphones), and it only costs cents. It is also very easy to add a headphone output to a speaker amplifier using a large serial resistor or a voltage divider on the speaker output.
Some people actually prefer the effect high output impedance has on the sound (mainly because it tends to boost bass with most full size dynamic headphones), so adding it as an option can be useful. Also, some older headphone models were designed for a specific high output impedance, for example the IEC standard (from 1996) 120 Ω.
High impedance headphones need more voltage for the same power (and therefore same SPL assuming identical efficiency), because P = V^2 / R. Since many modern sources (common portable players like the iPod in particular) have rather limited voltage output, they would not be able to drive most high impedance headphones to sufficient loudness for many people's tastes. Since for most listeners louder also sounds "better" in a non-SPL matched comparison, lower impedance (and therefore usually louder from the same voltage source) headphones are made in the hope of increased sales.
However, there are also practical limits on how low the impedance can be, because if it is too low, then both the maximum power will decrease (because of limited current output, and the output impedance acting as a voltage divider), and the sound quality will degrade (distortion will be higher, for example, output impedance will have more effect, and with capacitor coupled outputs there will be more bass roll-off) as well. It also drains batteries faster, and in extreme cases a very low impedance and inefficient load could even damage a source. So, 16-64 Ω has become the "standard" for the majority of modern headphones, with 32 Ω being the most common.
Selling the same headphone in different impedance versions allows for choosing one that suits a particular source the best (e.g. 32 Ω for the iPod, and 600 Ω for an AVR headphone output with high maximum voltage but also high output impedance). A higher impedance voice coil allegedly has a minor weight advantage as well because of the thinner wire, but opinions on this seem to be divided. Finally, it could also be a marketing trick in the hope of selling the same headphone to a single consumer more than once (i.e. someone buys the 32 Ω model first, and maybe later "upgrades" to the 600 Ω one).
The efficiency (in dB/mW) is not directly affected. However, the SPL from a given voltage in most cases decreases with increasing impedance. This is not always the case, because sometimes a high impedance headphone is sufficiently more efficient than a low impedance one that it still sounds louder from the same voltage source; some examples of this are the 250 Ω T70 vs. the ~60 Ω K701, or the ~50 Ω HE-6 vs. almost any higher impedance dynamic headphone.