how does current work in an amplifier?

It just depends on the amp-speaker combination and how high a listening level you prefer. Once the power supply of the amplifier is maxed out, the output signal voltage is not going to be able to match the input signal waveform, ie. distortion. The bass requires the most power, so it is the bass that starts to sound flabby or weak. At least, that is my experience...

The KISS answer to your second question is YES. An amplifier rated for a continuous 4 ohm load should handle 4 ohm nominal speakers better than an amplifier that is only rated for a continuous 6 ohm load. You're probably safe to make comparisons within a brand, but I don't think advertised specs really mean much when comparing different brands.

Looking at the question from an 'ohms law' perspective, it is a red herring question.
Even my (alleged) current hungry Magnepans have only a 4 amp fuse on the mid / tweets. Say the low is good for 6 amps.....so the speaker can take a total of 10 amps.
I2R=watts.....so 10*10*5=500 watts at about 5 ohms. That's about it.
Well, the other way to go about it is to MEASURE your speaker. I stuck a DVM on my panels......About 8vac was about the highest value I saw flicker by. Say I double that to 16vac. Since Watts=E2/R That gives me just over 50 watts.
I'll give everyone the benefit of the doubt and double that twice for 200 watts per channel into my panels.
That, sir, is loud....no LOUDER
That is why my opinion, strongly held is that amp amps while not meaningless sure depend on the ability of it to drive those amps at a reasonable voltage to provide POWER.

Don't forget the SOR of a semiconductor. Safe Operating Range. You'd need a real bunch of 'em to sustain 50 amps at 50 volts..........=2500 watts.

Hi Magfan, I believe your DVM is giving you an average RMS voltage reading. It's response is not fast enough show you peak values. Also, if you were playing a sine wave, only then would it be an accurate RMS voltage reading. An oscilloscope is the only accurate way to look at peak voltage/power. Speakers are motors, not resistors. So they have impendance due to back EMF, not really pure resistance. The music signal is AC and so Phase Angle is part of the Impendance/Power Factor. On top of that, the crossovers play into the impedance and phase angle too. So you can see how things get really complicated from a math perspective.