everlasting doors = age-abiding entrances. The tabernacle (or tent) of David, on Mount Zion, was not ancient. This looks forward to the fulfilment of prophecy in times yet to come.
King of glory = Glorious king. The repeated question points us both to Psa_22:6 ("a worm, and no man") and to Psa_23:1 (The Shepherd).