The use of artciles - 'A' product or 'The' product?

There is only one product of the process, so use the definite article 'the'.

But you can say, for example, that blackbird, greenhouse, pickpocket, etc. are all products of compounding.

If you are considering the product, use 'a', if you are considering the process, use 'the'.

Im considering words (in general) produced through the process of compounding.

Then "A product of this process" would be fine?

Yes.

Therefore, in the previous version of the definition

"Compounding (sometimes also called composition) may be defined as a process whereby two or more lexical items (including nouns, adjectives, verbs, and prepositions) are combined to form a new complex word. The product, traditionally called a compound, functions grammatically and semantically as a single unit. "

the use of 'the' before 'product' was incorrect? It should be "A product, traditionally called a compound, functions..."?

I would have used "The result . .."

So you would write that way?

"Compounding (sometimes also called composition) may be defined as a process whereby two or more lexical items (including nouns, adjectives, verbs, and prepositions) are combined to form a new complex word. The result of this process is traditionally referred to as a compound. "

Can I say, for example, "The resulting word is traditionally referred to as a compound"?

Yes

But first you meant that you would use "The result" in this way: "The result of this process is traditionally referred to as a compound", right?

You asked " Can I say ...."

I told you yes.

Now relax and be calm. The meaning is the same.