That is not quite right, but I think you are misunderstanding the conversation.
The number of samples you take directly correlates to the maximum frequency that is captured… because frequency is “number of oscillations per second,” and sample rate is “number of samples per second.”
It sounds like you think, though, that what we’re saying is higher sample rates will make the recording higher frequency - that is not what is being said here at all. What is being said is that the number of samples taken affects the RANGE of frequency that is captured. It is equal to half the sample rate, so a sample rate of 44100 Hz is equal to a maximum frequency range of 22050Hz - which is beyond the maximum range of human hearing. As stated earlier, the extra bit is there is nice for dithering, which is another topic that is beyond the scope of this thread, I think.
Not quite. You get most of your accuracy and detail from your bit rate, not your sample rate. An 8 bit sound is much less accurate than a 16 bit sound, and sounds noisier because there are larger jumps between the values of each sample in your curve. This is especially pronounced in 8 bit vs. 16 bit (as opposed to 16 bit vs. higher rates). Signed 8 bit has a minimum value of -128 and a maximum value of 127… when your wave is converted (since it is typically represented as -1 to 1), that means that you have a whole lot of graininess in your sound because the jumps are relatively huge. Once you get to 16 bit, the gap of 1 bit in the total range is pretty small (because the minimum value is -32768 and maximum is 32767), and while noticeable to a discerning ear, isn’t a huge deal.
Now, at a low sample rate, yeah, it will lose quality, but that is because you lose frequency range. For example, if your sample rate is half of CD quality, 22050Hz, then that means the highest frequency you can capture is 11025Hz - which is actually pretty low, you lose almost all of your sizzle and most of your hats that way.
However, any sampling above 44100Hz is outside the range of human hearing, except for particular (rare) mutations. I suspect if you were playing an old folks home, you could probably sample at about 33100Hz and do just fine. 
