Terminological hell in music

I have the immense joy of listening to Katja play many songs on the piano by ear. She picks them out perfectly after several tries using both black and white keys. I reflect on my own challenges in learning music as a child. When I tried to play on my Casio 210 sound tone bank I never played the black keys. It was as if they were in another class of toggles that needed special permission to depress. I never had the level of support that she does (from her mother and me), but as I help her I am refreshed in my memories of music from my childhood. For example, Why, WHY, is the Key of G-Major the key of one sharp? And why is that sharped note F#? It should be called the Key of F#. Or if it were to be organized by alphabetical order then a key with no sharps should be the Key of A (they partially got this right with A-minor) and then the key of one sharp should be the Key of B, two sharps would be the Key of C, and so forth. The terminological labels are out of control in music.