Ye, the order matters. This can be seen in chromosomal translocations which can cause cancer. A example for that would be the translocation of IRF4 which happens in a subtype of multiple myeloma. The translocation is permanently activating the transcription factor. See here for details:
The main reason for this is the regulation of the genes - when the order is changed, the regulatory elements which are important for regulating the expression are missing. A lot of these regulatory elements are located many kB away from the gene and are still important for its activation or silencing. This can look like the image below (image from here):
Regarding the mouse question: The orderOn which chromosome a gene is located is not really important - theif you compare different species. The gene I worked on for a while is functionally equivalent between mouse and human (the human version works perfectly in mouse), but they are located on different chromosomes. It again comes down to different regulation and in some cases also a different amino acid sequence. Also mice (as other animals as well) have quite a number of genes which are unique for them and which make a difference between the two species. There are a few interesting papers on that topic: