Sere, Since you are comparing A and C as nations, A would be a 'representation of democracy'. Your sentence would be, "...A, a representation of democracy, sees C as both a partner and a rival." If you were describing A's form of government, then you would say 'representative democracy'. Ex: "A is a representative democracy because instead of eveyone voting on every issue, citizens elect their chosen representatives to look after their interests."

1. Yes, alongside works well here 2. Representative is a person that represents something. "She is a representative of her school." She represents something, the school. She is a proxy for them, speaks for them. Representation is a thing that represents somethings values, opinions, etc. "This modal of our town is an excellent representation of how hard she works." It represents something, for example, how hard she works. Here is how I would rephrase your statement: Alongside the biggest ocean in the world, C and A are the two greatest players in the game of world order. A, a representation of a democracy, sees C as both a partner and a rival. I use "representation" because democracy is a set of values and ideas.