Yes, you can sell something and not make a profit, but the goal of commodity production is profit, not equal output from input. The Capitalist has no reason to pay people just to break even, the goal is profit, and as economies are measured as aggregates, that is the purpose of commodity production.

Communism is a post-Socialist form of economy. Socialism is defined as Worker Ownership of the Means of Production, while Communism is a Stateless, Classless, Moneyless society.

Trade unions are a good thing, but not Socialism. Socialism requires ownership. Unions help offset some of the issues of Capitalism, yes, but until you get rid of the Capitalists, it's still Capitalism.

Yes, you're a right winger, because you are supporting Social Democracy as a framework. Social Democracy is Capitalism with expanded social safety nets, there are still Capitalists, still Capitalism, and very little worker ownership, but it certainly sounds nicer than what the US has!