With future perfect (F2) you jump to a point in the future, turn round and say some action is finished then. Actually a complicated thing and cumbersome and in most cases you can express the same idea much simpler without using F2. This tense existed in Latin and it was imitated by writers.
In current English usage, muse can refer in general to a person who inspires an artist, writer, or musician.
Inspire is to make (someone) want to do something; to give (someone) an idea about what to do or create. See Miriam Webster Dictionary Online. We've lost the depth of the latin root from which inspire comes. Webster's 1828 Dictionary is a great place to go for traditional English definitions of words.