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I'm not sure I have this straight in my head yet. In this sentence, is it correct that "son" is nominative (or is it accusative??), and "woman" is genitive, being possessive, and "that" is also genitive because it's describing the genitive woman?? Also, how important is word order? Is any word order understandable, even if it changes the emphasis, or are there rules?
In sentences where you only say that something is something, X = Y, there is no object a no cases, only nominative. Matěj (nominative) je syn (nominative). The "je syn" part is called a predicate. It's the same grammar as saying Matěj (nominative) je mladý (young, nominative).
And yes, "té ženy" (that woman's or of that woman) is genitive, showing possession. Both words (ta žena) decline together.
Word order is fairly important, it expresses things that are expressed by articles and by intonation in English. If you get the word order wrong, it depends on how wrong it is - how different from the right now. You will usually be understood anyway, but it can be confusing (try undestaning this: Usually will understood you be, but confusing be can it).
Here we have two entities (nouns or names) connected with a linking verb "je"/"is" ( https://en.wikipedia.org/wiki/Copula_(linguistics) ). In these cases both elements ("Matěj" and "syn") are in the nominative case.
Much later in the course you will see that the noun predicate can also be in the instrumental case, but I suggest not to get too distracted by that.
So the basic phrase is "Matěj je syn" where Matěj is the subject and "je syn" is the predicate or a verb phrase.
"ženy" is then a modifier that expands the word "syn". It is just like English "of (a) woman" and the genitive case is used here.
Finally, the demonstrative "té" in "té ženy" is like "that" in "that woman" and it follows the case of the noun it is connected to, here the genitive case of "ženy".
I fany of those terms are unfamiliar to you, you can read more about them on Wikipedia.
https://en.wikipedia.org/wiki/Verb_phrase is an optional bonus