No problem, thanks for asking! 🙂
One thing I think you're misreading is the State withering away. What we commonly think of as the "State," ie the entire public sector, government, administration, etc is not the same as what Marx calls the State. For Marx, the State is the elements of Government that contribute to Class oppression.
Before we can continue, we need to know what a "class" even is to begin with. Elsewhere in this thread, people make reference to something like a "planner class," but for Marx, no such thing exists. Rather, Classes are social relations with respect to ownership of the Means of Production and interaction with it. "Plumbers" are not a class, just like "managers" are not a class. The reason this is important, is because a classless society is one that holds all of the Means of Production in Common. In other words, full Public Ownership.
Circling back to the State, how does it "wither away?" The answer is that the Proletarian state, one dominated by the Proletariat and not the Bourgeoisie, gradually wrests from the Bourgeoisie its Capital with respect to the degree that it has developed. A Socialist revolution would not turn everything into Public Property instantly, markets and Capitalists would remain until the industries they govern develop enough that Public Ownership becomes more efficient and markets stagnate, ie monopolist phases where competition has run dry.
Since this is a gradual process, imagine every bit of Private Property wrested chips away at the State. The second Private Property reaches 0% and Public Property reaches 100%, there are no longer any classes, and thus no class to oppress. The "State" disappears, leaving only government, administration, and more behind.
As for the structural makeup of the socialist government, it would be most likely made up of "rungs," a local rung, a regional rung with representatives from each local rung, a provincial, national, international, etc rung, as many as needed and as few as necessary for proper Central Planning. What you describe as people being able to just "take advantage" of that could happen, Communism isn't some utopia of perfection, but such a society is far more resiliant as well as resistant to this than Capitalism, and more importantly builds up over time in a realistic manner.
Does that answer your question? Feel free to read from the reading list I linked earlier, also linked on my profile!