As the title says, I am aiming for getting my map ranked. But I notice that my "normal" difficulty does not have 2 stars diff rating(it's 1.87). Do I need to increase the difficulty so that it reaches 2?
No, there are no star rating requirements for maps to get ranked. The star rating doesn't always represent the actual difficulty of the map so it's not taken into account. As long as your map is mapped like a Normal difficulty, it's okay.
Star rating isn't a perfect system. Idk about mania, but would say if the map feels like a normal, then it's a normal, regardless of what the game says it is, as long as the difficulty spread is linear.