We are using the grayscale-filter for images, which is working fine so far. Additionally we want to adjust the contrast of the images and support an "invert-function" that actually inverts the grayscaled image. Does the product designer already support this feature?

If not: Is there any option to add "custom" modifiers with a custom jQuery-Script to the designer?

FPD does not come with an invert filter, sorry. You can of course add custom code, yes. http://jquerydoc.fancyproductdesigner.com/