Some difficult questions about Zzzip and EXOS, but one easy question about English, which I will answer first.
We can use the word "mirror" to mean "reflect", although for a list of commands, such as in your program, we would simply say "mirror" rather than "mirroring". However I think we would nornally use a different word. I often edit photos with Adobe Photoshop, and that program has a number of rotate commands, two of which are Flip Vertical and Flip Horizontal. (Not very good English really, as Vertical and Horizontal are adjectives - after a verb it would be better to use the adverbs Vertically and Horizontally). Anyway these commands are identical to the functions in your program. Because it is not so obvious in your program that the commands are meant to rotate the image, I would suggest that you use the commands "Flip Image Vertically" and "Flip Image Horizontally".
I will have to do some more work to try and answer the difficult questions.