I keep wondering if dodge chance is any of these because the tooltip says "ships evasion" which would indicate that multiple ships are affected by one's ships engine/shield.

Ship "Evasion" is technically just a penalty to enemy accuracy if I remember right

Yes, even though ennemies will always have a 5% chance of hitting. It applies to all ennemy ships, but I do not know if the bonus to give malus accuracy to ennemy ships is limited to only the equipped ship or if it is flotilla wide, or fleet wide.