I am currently working in my PhD thesis, and it became necessary to understand some facts about free symmetric operads. Hence I started to study this subject by myself, following Kapranov & Ginzburg's paper (Koszul Duality for Operads) and the Bresse's paper (Koszul Duality of Operads and Homology of Partition Posets). Naturally, a few doubts has arisen. Since I had a couple of questions on this topic unanswered in math stackexchange, I will post my new questions here - they are not so trivial to me, but I think that they are probably routine for researchers.
My first question concerns the intuition about this topic. Usually in algebra, the operations in free structures are described via concatenation, e.g., on free groups, on free algebras, etc. Keeping this in mind, I thought about the operad product (on free symmetric operads) as a concatenation via tensor products, where the trees play a similar role in operads as the "reduction rules" in free groups, in order to guarantee that the axioms of the operations are satisfied. This analogy makes any sense?
Now, my second (and more technical) question is about the construction of a free symmetric operad, as done here (pages 69 to 71). What exactly are the elements of the $\Sigma_n$-module $F(M)(n)$? Also, how to explicitly describe (i.e., in elements) the operad product on $F(M)$?