I always heard that there is a prohibition on listening to the words of a song that is not praise and thanksgiving to the Holy One, blessed be He. Have you ever seen a Haredi rabbi listening to Michael Jackson? Or even in Hebrew, have you ever seen a Haredi person listening to Omer Adam? That seems to show there is something behind it, no?

Is it permitted to listen to a woman when I do not know what she looks like?

Have you ever seen a Haredi rabbi wearing a T-shirt? Surely there is also something behind that, no?
A woman's singing voice is a different matter. In my opinion there is no formal prohibition here, only a concern about erotic thoughts. Check yourself and think whether it leads you to such thoughts or not. And even if it does lead to such thoughts, if you are going for the art or the enjoyment of the music, then there is room to permit it on the grounds of "it is unavoidable and not intended."

Let me push in a little on the side, because I have long had a great puzzle about mixing melody with song lyrics. I love poetry and read a lot, and I like melodies and listen from time to time, but a melody with words is like a camel-donkey hybrid: the words they set to music are usually mediocre and not the best poetry, and the melody too, since it is bound to the words, is not the best it could be. It is like looking for restaurants where, during the meal, they also give you a foot massage. The food probably will not be the tastiest, and the massage will not be the most successful.

Haha, got it, thanks.

Actually, in my opinion there is something about a melody that blends well with the words and lifts the song to another level and highlights certain aspects of the words.
And the reverse as well: many times there is a beautiful melody to which the words give meaning.
If I use your example, then maybe the food will not be the tastiest one possible, although not necessarily, and the massage will also not be the absolute best, same there,
but specifically the combination between them will create a special experience that improves both the food and the massage, and that you can get only if you do both together.

Why go for a massage? As is well known, the taste, smell, and texture of food come together to create the enjoyment. If one is missing, the whole is missing.

But it is possible, and easy, to find words on their own that are better than all the words in songs that are set to music, and it is possible to find melodies on their own that are better than all the melodies in sung songs. Is it worth giving up quality in each part for the sake of the combination? To my taste, no. I, for example, read poems at times of certain moods, and I often listen to sounds when I work and study and concentrate, but at no time do I feel like hearing sung words. And in our little world, in almost every covered space at almost every hour, everything is full of sung words, while most people do not read poems and do not listen to symphonies. I do not really understand this, and the matter gives me a feeling of autism.

I did not understand what authority the medieval authorities have to be lenient here. If the plain sense of the Talmud is that it is forbidden, then it is forbidden!

As I answered you elsewhere, sometimes we are lenient against what appears in the Talmud. There are also contradictions between Talmudic passages on this issue. About that, perhaps among other things, it was said: custom follows Jewish law.