Graphics optimisation - Project 1

I have image files attached, which I want to optimise/crush/compress as much as possible to reduce filesize. It is critical that they remain in their correct formats, and in the highest quality possible - so I'm seeking a method/software that radically changes the filesize without reducing quality (of course, removing unused colours etc is ok)...transparency is very, very important. If it is a PNG32 file, it is critically important that the transparency (including transparent gradients) remain without noise, banding, white etc. I cannot accept images which are lower filesize, but sacrifice visual quality. Please keep files in the directory structure provided. Thank you