Hi Andy,
For of the Image Analysis window, the input layers take precedence over the default ArcMap settings. So if you change your input layer with contrast and brightness, and then clip (for example), then the clip will also have these contrast and brightness settings. These settings come from the top layer in the layer list. I think this is done to preserve the changes you have done to the layer.
Regarding the resampling technique, this is done through display resampling at this point. Note that you can easily change the mosaic method (min, max, blend) even after the new layer is created by simply selecting the new layer and then changing the mosaic method on the image analysis window.
I hope this helps.
Robert