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.
late 14c., protectors of the arts, from Old French Muse and directly from Latin Musa, from Greek Mousa, the Muse, also music, song, from PIE root *men- to think, remember (see mind (n.)). Meaning inspiring goddess of a particular poet is from late 14c.