Using with other applications

I'm not familiar with the Muse, but I export Illustrator files as SVG or DXF files to use with other vinyl cutters. Somewhere in the instructions it should tell you what valid types you can use.

I can't see why not. Years ago I use to work for an inflatable company. They used their very large cutting table to cut materials for large inflatable balloons. I believe they also used it to make vinyl stencils for their balloons and signage for banners as well. However they just used a free vector program to control their machine, but I'm sure you can use Illustrator for this as well. Probably better for you in the long run since most of those free vector programs usually have bugs in them.

Hope that helps.