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.
That he manages to keep his literary Uber on the road and out of the ditches is a tribute to his skill as a writer and storyteller. Muse is a kind of mystery: not so much a who-done-it but a more satisfying who-felt-it, who-experienced-it, who-saw-it-for-what-it-really-was . . .