How can anything be communist which exists only to produce commodities for market? I told my students that this surplus crop would not be a commodity because it was not produced for the PURPOSE of market exchange.
As I understand Marx, a product of labor that has utility for someone in any community and that passes through a market exchange to move from the producer to the consumer is rendered by that passage a commodity. This commodity status is not removed or undone because the producer also engages in production of useful objects that do NOT pass through the exchange process. So, for example, because a worker today produces all sorts of goods and services inside his/her household which are consumed there without any exchange process, that fact does not affect the part of his/her time in which he/she engages in production of goods and services that are produced and exchanged. You are right to raise the issue of whether exchange is occasional or regularized - as Marx did - but while that is historically relevant and interesting for concrete empirical analyses, it does not, I think, impact the definition of commodity.
Let me jump to your last question since it is related again to the definition of commodity. To say some produced good or service is a commodity refers to its passage through an exchange (quid pro quo) process. That, by itself, says nothing about the class process - the relations of production - out of which the commodity emerged. Thus, self-employed craftspersons can and do produce commodities, as do feudal plantations, slave-masters, worker communes, as well as capitalists. The conflation of commodities and exchange, on the one hand, with the class relations of production, on the other, is a theoretical move that Marx worked hard to criticize and avoid in his own work. The critique of markets is one thing; the critique of exploitative class structures of production is something else. Little is gained and much lost in losing sight of that difference. Once the class structures of capitalism have been overcome in favor of, for example, workers themselves collectively appropriating and distributing the surpluses they produce, they will have to determine whether to distribute the resources they need for production and likewise whether to distribute the products they produce by means of markets and/or other mechanisms of distribution (markets being merely one kind of such distribution mechanisms). Most societies (modern capitalism very much included) have opted for mixtures of markets and other mechanisms to distribute resources and products. In terms of your question, then, if and when workers' collectives produce goods and services which they exchange in markets, that would be a communist class structure coexisting with market exchange. That coexistence would entail its particular contradictions just as the coexistence of capitalist class structures and markets generates its particular contradictions (competition, business cycles, etc.).
Lastly, apropos your comments re China and Albania, while I can see and applaud the requirement of leaders and cadres knowing via direct experience something about the daily lives of the masses, that is a different matter from reorganizing the class structure of enterprises throughout an economy such that the productive workers within them - those whose labor generates the surplus - are likewise identically the people who collectively appropriate and distribute the surpluses they produce. That fundamental transformation of enterprises represents the "revolution" in class terms derived from Marx's work. Of course, such a micro-level transformation requires and will support macrolevel changes of the sort classical Marxists have for so long stressed (without, however, adding the microlevel transformation I refer to). Thus, socialized property in means of production and economy-wide planning - if they are to be part of a communist transformation - MUST include the micro-level transformation inside enterprises or else the result can be a socialized and planned capitalist class structure and one that can very likely evolve such that the retained capitalist class structure inside enterprises (even inside state enterprises) eventually undermines the socialization of productive property and planning (as in the history of USSR and Eastern Europe, etc.)
To get the full statement and argument for the above summary, please take a look at S. Resnick and RD Wolff, CLASS THEORY AND HISTORY:CAPITALISM AND COMMUNISM IN THE USSR, London and New York: Routledge Publishers, 2002.