My Minecraft skin will not change
Solution 1:
Sort of recently, you can change your skin through the minecraft launcher. Basically you start the launcher, press skins. Then you can choose your image and upload it. It may take some time before the changes are actually applied.
I have assumed that you use the Java Edition and the latest launcher.
About the 'Bad Request': Perhaps Mojang has removed the functionality to change skins via the website, but I can't say that for sure.