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.
A MUSE is someone who is an inspiration to another person. Say there is an artist, they have regular periods of boredom and mind blanks, when they can't paint anything. Then there is a person, and for whatever reason, this person brings the artist much inspiration.