Although age-related hearing loss is not the norm, it's a quite common condition:
Results showed that the prevalence of central presbyacusis increased
with age and that the highest prevalence was a striking 95 percent in
the 80+ year age group.
The rest of my answer is based on this book, some parts of which exist online (which I'll quote). I'll be referring to this part of the website specifically.
Sklivvz already answered your first two questions, but here is a graph to illustrate it as well:
Consequently, patients with age-related hearing loss often have
normal sensitivity at low frequencies, but progressively poorer
sensitivity for higher frequencies, as shown here:
As you can see from the graph, severity of age-related hearing loss depends on sound frequency: older people need high-pitched sounds to be displayed more loudly, in order to hear them.
3. Does that mean high frequency sound become less harmful as we become older and older?
It actually does! But that's because the harm has already been done...
It's not described much on the website, but the book explains that there is a relationship between how loud a sound has to be to harm you, and which frequency it is. Sounds that are near our auditory thresholds (under 20 Hz and above 20.000 Hz in the normal, healthy hearing range) can't harm us even if they are extremely loud. We don't hear them because they cause no mechanical change in our ear that responds to those frequencies, and consequently no harm is done. In the case of age-related hearing loss, the hair cells in the inner ear that should respond to high-frequency sounds, have already stopped responding, so there is nothing left to harm.
Here's a plot of the connection between loudness and frequency in auditory perception, in which you can see that sounds around 4kHz can most easily harm us. Human speech is at this range, so we're particularly sensitive to it:
Does this explain that when I was younger, I was more sensitive to sound and slept less well?
Probably not, except if it was mosquitoes that were keeping you up.
Does this fact indicate some trend of our change of music taste over the time?
I don't see that it does.