If “Mystic Swordsman LV2” attacks a face-down Defense Position monster, that monster is destroyed by “Mystic Swordsman LV2”’s effect, not as a result of battle. So you cannot use its second effect to Special Summon “Mystic Swordsman LV4” during the End Phase.
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.