You can't have Communism in one country, as Communism must be international, global, and have fully eradicated Private Property and Commodity Production. You absolutely can have Socialism in one country, however. Socialism is a transitional status towards Communism from Capitalism, and is dependent upon human supremacy over Capital and a trajectory towards further collectivization and the dominance of the Public Sector over the Private not in percentage, but power.
To take the opposite claim, that you can't have Socialism in one country, is to determine that you must call a fully publicly owned economy "Capitalist" despite eradication of Markets and commodity production in general. Further, to claim that Socialism can only exist internationally is to make the asserted claim that a 99% publicly owned and planned economy is actually dominated by the 1% in the market sector and is thus Capitalist, these are anti-dialectical judgements.
Further, revisiting Marx, he considered countries where feudalism was still the majority of the economy yet Capitalism well on its way to dominate the entire economy to already be Capitalist. The dialectical method acknowledges that there is nearly no such thing as a "pure" system, to require "purity" for Socialism alone and not any of the previous Modes of Production erases the foundation of Scientific Socialism.
All in all, I am getting a definite Trotskyist vibe from your analysis and that would explain your stances a bit more, but I really do wonder in particular how you personally reconcile Dialectics with an anti-dialectical approach to Socialism specifically. The productive mode does not depend on a "one drop" rule of commodity production, but the dominant mode and the trajectory of the system as a whole.
I suggest reading What is Socialism? Here's a relevant snippet from it talking about your exact argument:
Let’s imagine trying to apply this line of thinking to any other mode of production. If any hint of private ownership, commodity production, and the anarchy of production in a socialist society would serve to prove it is not socialist, then, by logical necessity, any hint of public ownership, social production, and economic planning in a capitalist society would serve to prove it is not capitalist. Real capitalism, therefore, just like socialism, can be proven to have never been tried.
This also leads to another absurdity. There is an enormous gulf between these two systems. How, then, does one transition between capitalism and socialism? If a mode of production can only exist in its most pure form, then how does one mode of production transition into the next? Necessarily, it must be an instantaneous jump, from one pure form to another. It fundamentally cannot be any other way.
I think you're a bit confused about what "State Capitalism" is in Marxian economics, here. Marx and Engels both repeatedly asserted that folding Capital into the Public Sector is a gradual process once "lower-stage Communism" (now referred to as "Socialism") was achieved. This directly implies markets and Private Property exist even within a society that had already become Socialist. I am not sure how you can counter that without attempting to redefine Marxism or reject it wholly.
As for the nature of the PRC's economics, the Public Sector is primary, and the Private Sector is gradually more heavily influenced and planned by government. This does not mean it's "impossible to get relief because the CPC is their boss," the CPC is not run for profit like that. SOEs compete in the Private Sector, but the CPC itself is not made up of the bourgeoisie, but overwhelmingly not bourgeoisie.
I think reading theory would help you a lot with understanding how the PRC operates and why.