How does a fungus protect itself from digestion by other fungi?
In general fungal cell walls are resistant to whatever enzymes or compounds they are excreting to break material down for consumption. Conceptually, it is a little like your stomach lining being resistant to stomach acid. For a more detailed answer you may have to head over to your local university and find a Mycologist.

There is ongoing research on how fungi actually "eat." You can look up fungal endocytosis if you wish to research it more. There may be other mechanisms as Shigeta mentions.