Not exactly correct, but not far off.
CDs have always been 16 bit, 44.1khz sampling rate. 44.1 refers to 44,100 samples per second, so each second of audio is divided into 44,100 sections of audio. 16 bits refers to (simply) the dynamic range of the sample. It was correctly noted that 16 bit sample depth give you 65,536 possible levels of "gain" from -∞ up to 0dbfs.
It is also correct that a sample rate of 44.1khz allows for a maximum frequency of 22,050hz (makes sense, right? The most oscillations that 44,100 samples could cover is one positive and one negative cycle). This is mostly theoretical though, as all CDs only cover 19,980hz (20hz to 20khz).
As a recording engineer, I much prefer 24bit 48khz recordings, as they offer 16,777,216 levels of dynamic range, and a theoretical 24khz of frequency range. They do actually sound better, too. Especially for musical recordings. But really, more importantly than 24khz of total range, is more "space" in the middle range frequencies for detail and nuance.
Same goes for 96khz, and to a point, 192khz recordings.
Now for the really interesting stuff, 1 bit audio is a thing! To make it work, though, you need incredibly high sample rates, in the order of 2.5MHz (2.5 million samples per second) to get it to really work. Some light reading:
https://en.m.wikipedia.org/wiki/Direct_Stream_Digital
Neat stuff!
Also, you are correct, any digital sampling of an analog wave will leave out some information, but as long as there is enough information to extrapolate a wave, it's usually pretty accurate.
Vinyl, or any truly analog audio source, does technically represent the analog source material more accurately, but there are so many other variables that go into the source recording quality and playback equipment quality that I'd bet that it would be hard for most to tell the difference between a well mastered CD and a clean Vinyl.
