The most important thing to remember about these masks are that they are essential made with paper. As such, exposure to water for any length of time isn't recommended. I DO seal every single mask, so they are water resistant. They are NOT WATERPROOF.
If you think about that, mask treatment should be fairly obvious. Don't wear them in rainstorms, showers, or very humid areas. When cleaning always blot, NEVER SCRUB and don't leave something wet laying on the mask.
Store the mask in a clean dry place.
In most cases the ties, ornaments and feathers are adhered to the mask with hot glue. If something comes loose, carefully remove the excess glue and use a hot glue gun to fix it.
If the finish of a painted mask is damaged in some way, that area can be repainted using acrylic paint (the cheap bottle stuff is fine). Then sealed using a good quality clear glossy spray sealant or Modge Podge if you prefer.