Help ID buttons

[Shiny]

Hi All,

I have been having a sort out and found some buttons at the bottom of my badge box, can anyone help me with them.

The first one is an RAF one but am I reading the maker correctly, Buttons Ltd B'Ham? and is there a particular reason why the bit you would sew it to the uniform with is flat, almost squared off?

The middle small one is brass with a scrap of khaki material attached but I don't know what it is.

The third is also small, I'm guessing light infantry?

Thanks for the help,

Michael