If “Light of Intervention” is active, you cannot Normal Summon “Mystic Swordsman LV4” because it can only be Normal Summoned face-down, which “Light of Intervention” makes impossible to do.
If “Mystic Swordsman LV4” attacks a face-down Defense Position monster, you destroy the monster with “Mystic Swordsman LV4”’s effect before flipping the monster face-up. Effects like “D.D. Warrior Lady” cannot activate.
If a level monster fulfills its condition to Special Summon the next-highest level (for example, if “Armed Dragon LV5” destroys a monster as a result of battle), and the level monster is then flipped face-down, or removed from play permanently, or sent to the Graveyard and then Special Summoned from the Graveyard, then its condition is reset and it is no longer considered to have met the condition to level up to the next level.