Short answers, pulled from the story.
Apollo was prominently considered the god of music and harmony. Several legendary gods and demigods created aspects of music or contributed to its development, but Apollo held this specific role.
The sarcophagus of Hagia Triada shows that the aulos was present during sacrifices as early as 1300 BC. Music occupied an important role in Greek sacrificial ceremonies throughout history.
The lyre served as the conventional training-instrument for an aristocratic education while the cithara was a professional version used by paid musicians. The kithara had a box-type frame with strings stretched from the cross-bar at the top to the sounding box at the bottom.
Pythagoras invented the monochord which has a movable bridge along with a string stretched over a sounding board. Using the monochord he found the association between vibrations and lengths of strings after studying sound hammers made in a blacksmith's forge.
The Eleusis inv. 907 trumpet signal survives from Classical Period while Papyrus Ashm. inv. 89B/31 and 33 contain citharodic nomes from Hellenistic Period. Delphic Hymns survive as stone inscriptions with music notation lines above main Greek lettering.