QWill this follower's Fanfare ability trigger if I put it onto the field with Wildwood Matriarch or Lymaga, Forest Champion's abilities?

AYes. Those abilities directly "summon" the follower to the field.

QWill this follower's Fanfare ability trigger if I put it onto the field with Octrice, Omen of Usurpation's activated ability?

ANo. Octrice's ability involves the player "playing" the selected card, so it isn't put onto the field by the ability itself.