However, it seems my understanding of audacity tools seems to be quite poor,
This isn’t all Audacity-specific but here’s some basic information:
0dB is the “digital maximum”. It’s the highest (integer) you can “count to” with a given number of bits. It’s the maximum for your analog-to-digital converter, digital-to-analog converter, and regular (integer) WAV files, etc. You can have “bigger numbers” with 24-bit file compared to a 16-bit file but everything is scaled by your drivers to match the actual bit-depth of your soundcard so a 0dB 16-bit file plays at the same volume as a 0dB 24-bit file. If you try to go over 0dB (with integers) you get clipping (distorted flat-topped and flat-bottom waves).
Audacity uses floating-point internally so it’s virtually impossible to clip inside Audacity. But if your data goes over 0dB you can clip your DAC if you play-back at full-volume and you’ll get clipping if you export to a (regular) WAV file, or make a CD.
Audacity will “show red” for potential clipping (or real clipping). But, if you have a clipped file that doesn’t hit 0dB because it’s clipped for some other reason, or because it’s been attenuated, Audacity won’t show red… It’s not looking at the wave shape, it’s just looking at levels.
Amplification (and attenuation) and Normalization are both simply linear volume adjustments. The whole file (or the selection) is adjusted up or down by the same dB amount. Typically, you use one or the other…
Normalization is “smarter” because it figures-out how much adjustment to make to hit a particular peak (usually 0dB, although Audacity’s version defaults to -1dB). Audacity’s Normalize effect also has a couple of additional features/options (remove DC offset and normalized left & right independently).
But… Audacity’s Amplify effect is also “smart”. Your file has been pre-scanned and Amplify will also default to whatever amplification (or attenuation) is needed to normalize the file.
GoldWave (a commercial competitor to Audacity) uses the term “Maximize” instead of “Normalize”. That’s logical and maybe less confusing, but everybody else in the audio world says “normalize”. Some people (and some software) say “normalize” to when they mean “volume matching”, but that’s the wrong terminology… Normalization is from a mathematical concept related to the peaks values, not “loudness”
As you’ve discovered, the peak levels don’t correlate well with perceived loudness. Loudness depends more on the (short term) average and the frequency content. Most commercial recordings are compressed to make them louder.
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Dynamic compression makes loud parts quieter and/or quiet parts louder. (It’s non-linear.) Typically, compression is used to make “everything louder”… First, the peaks/loud parts are “pushed down” (compressed). Then make-up gain is used to bring-up the overall/average volume making it louder overall.
Don’t confuse this with file compression like MP3. 
Limiting is a kind of fast-compression, and it’s also often used with make-up gain to make “everything louder”. In my limited experiments (pun ) the Audacity limiter seems to be very-good, and since there are fewer settings to mess with it’s easier to use than the compressor effect.
Clipping is a (usually bad) kind of dynamic compression.
If you are making music “at home” you probably won’t get the same loudness (with as little “damage”) as a professional mastering engineer with years of experience and expensive tools. But, you can get enough loudness to meet audiobook standards. (IMO - Lots of modern music is over-compressed… It’s one-constant-loudness throughout and that makes it’s boring and it makes me want to turn-down the volume control, or turn it off!)