Guy, my thoughts are as follows:

On conceptual structure, a concept may be (and often is) defined in terms of other concepts. But the idea of a concept as "built out of" and "therefore reducible," this seems to be a confusion of theory and concept.  The concepts are the factual, empirical terms in a theory, which also comprises logical terms (if/then, and/or, up to higher mathematics). The idea of "reducing" comes up when a developed theory (usually in physics) seems to explain phenomena that are also explained by another developed theory (we see it in chemistry and biology): What are we to make of the concepts in those theories. Do chemistry and/or biological theories address "emergent" concepts, i.e., empirical phenomena that emerge (??) from interactions of more primitive concepts?

Thus reduction of chem or bio to physics is a mapping of models demonstrating that chem/bio theories treat defined terms as primitive. The acceptance or rejection of reduction (of theories, not concepts) is the difference between methodological individualism and methodological holism. The former rejects emergentism.

On conceptual development, you seem to be talking about a theory of cognitive development, in which the concepts used in the theory (such as volume and density) have empirical import--they are operationally defined as concepts in the theory.  Whether one concept is somehow "prior" to another during the process of cognitive development would probably be a testable hypothesis derived from the theory.

In order to talk about concepts one would probably have to talk about expressions (see Mr. Bell's contribution). To do so one needs a metalanguage. The object languages one talks about in the metalanguage may be formal or informal or one may talk about several object language some of which are formal and some of which are informal. Concepts can than be seen as abstract objects relating to concrete objects (expressions/terms) according to some abstraction theory. Once this is set up, one can start talking about reducibility of concepts and understandability of concepts.

1. The reducibility of concepts (abstract level) will most straightforwardly be explained by the reducibility of expressions (concrete level). Reducibility of one expression to other expressions is usually understood as the first expressions being defined by the other expressions in a given language. Thus, reducibility of expressions and ultimately of concepts will be language relative. The reducibility relation will largely depend on the kind of language that we are dealing with, especially whether it is formal language or an informal one. Usually formal languages include explicit definitions while in informal languages we can only reconstruct definitions and there will be various ways to do so. Thus, even to say that density is defined by volume (and other expressions/concepts) is only one way to reconstruct our utterances in informal language (including the informal language we speak in physics class in middle school). In sum, with respect to natural languages it is very misleading to settle on specific reducibility relations between expressions and concepts.

2. With what I said in the first paragraph, understanding concepts will be explained by understanding expressions or knowing how to employ expressions. Similarly the acquisition of concepts will be explained by learning how to use expressions. Thus, when you ask whether the order of acquisition determines an order of reduction you have to take into account that the order of acquisition is not relative to a language while the order of reduction is. In addtion, if you relativize the order of reduction to natural language there will be a multitude of ways to reconstruct expressions and thus to attribute reducibility to concepts. Furthermore kids might learn the use of certain expressions in varying orders. Should each observed order yield another concept structure?

You ask two intertwined questions. One has to do with conceptual development; the other, with conceptual structure. To begin with, you can benefit from reading the following book: Conceptual development: Piaget's legacy by Scholnik, E., Nelson, K., Gelman, S., & Miller, P. (Eds.) (1999). Mawah; NJ: Erlbaum. Answers to your questions depend on what theoretical framework who adopts: Vygotskian, Piagetian, or Fodorian, to cite three examples. As you certainly know, for J. Fodor and many others (e.g., S. Carey) there is no conceptual development because our concepts are innate. This is an untenable stance. If this were the case, then how does one explain that some concepts (e.g., the volume concept) appear first than others (e.g., the density concept) or that some concepts (e.g., the proportionality concept) appears only at a later point in development (typically at adolescence)? It contradistinction, both for Vygotsky and Piaget there is conceptual development. For instance, Vygotsky sustained that, for example, what he called mediated memory appears only after what he called natural memory. In the same vein, according to Piaget, concrete operational concepts (e.g., the idea that the number of elements in a set remains constant regardless of their spatial arrangement in the set at hand) come only after preoperational concepts (e.g., that number depends on the spatial configuration of its elements in the set in question). Therefore, both Piaget and Vygotsky, just to cite two examples, accept that the more complex concepts are built out of simpler (more primitive, basic?) concepts. However, to accept this stance does not imply that the former are reducible to the latter. Suffice it to say that, for Piaget, for instance, his concrete operational concepts go well beyond his preoperational concepts, and that Vygotsky's mediated memory is much more complex than, and hence irreducible to, his natural memory. More to the point, according to Piaget, the link of formal operational concepts and operations to concrete operational concepts and operations is a logical, and even metaphysical link rather than a psychological and empirical link. This is so, because formal operations are operations on concrete operations. Because of this it would be a waste of time to run an experiment to test such an order of emergence. As formal operations are operations on concrete operations, it is true by definition that formal operations appear in development later than concrete operations. It is a sad reality that in psychology there are many experiments to test what is untestable because the hypotheses underlying such experiments are analytical propositions, and hence, not subject to falsification. This means that when we run an experiment we should examine first if the hypothesis or hypotheses we want to test are in fact testable or untestable hypotheses. As Wittgenstein cogently remarked in his Philosophical Investigations, in psychology there are experimental methods but conceptual confusion. As for conceptual structure, it may be interpreted in functional or structural terms. When the former is the case, conceptual structure is judged to be an antecedent in our brains/minds that is responsible for a certain order of acquisition of some concepts or the simultaneous emergence of concepts judged to be identical or similar to one another in terms of cognitive complexity. When the latter is the case, conceptual structure is judged to be a set of formal or logical characteristics (e.g., equilibrium, integration, differentiation of perspectives, dimensions, and so forth) that lies the heart of certain forms of behavior, thinking, and feeling. Parenthetically, it should be said that Piaget's overarching structures (i.e., structures d’ensemble) have been widely and wrongly interpreted in functional rather than structural terms. See my ideas on the standard (and erroneous) interpretation of Piaget's theory in a coauthored Psychological Review paper, titled. In defense of Piaget's theory: A reply to 10 common criticisms (see my publications in Research Gate).

I hope that these my considerations may be of some help concerning your both interesting questions.