Hi! It's called Etude Op. 10 No. 3 composed by Frederik Chopin. For the intro, I used the fullmetal alchemist version because I really like the sound of the oboe. I mixed it with the original machine for pigs main menu song and gave it a slight radio static effect. The ending C version is just a piano rendition of the same song.

What was the Ending A the song with the lady singing?

It's a song from the original machine for pigs soundtrack. It sounds like the demo version of the end credits. you can find it in this video at 43:20
https://youtu.be/aKSU5XfvtWE?si=ys6-cienMjTS1u5v&t=2599

Please tell me, what is this cheerful song playing on the radio?

It's called "The washing on the Siegfried Line"