Any added damage you gain from any source would not change the Tag of a skill.
All those conditional effects depend on the skills Tags, not on what stats you have on gear.
Further more, the %increased elemental melee damage would affect any elemental melee damage you have on gear or passives. Even if you using a skill like Vengeance or Rive, which don’t have an elemental tag, they would still get the increased flat added damage.