In a subordinate clause, the conjugated verb ALWAYS comes last (but before any additional verbs in the infinite form). In case you are having trouble working out the subordinate and independent clause, try saying both out loud without context. In this case, the independent clause, "Ich weiß nicht" = "I don't know", sounds alright by itself. But the subordinate clause, "Wessen Sohn er ist" = "Whose son he is", doesn't sound right at all.
The Owl doesn't introduce or identify homonyms like "weiß" unless you roll over them. It will show it to you one time for whatever definition it gives you first (so it shows "weiß" meaning "white" in Adjectives), and then it never gets around to showing you the other meanings (as a form of "wissen").
This source explains it somewhat well. In English we only need to put a comma in if the subordinate clause comes first (although that is dying out too). For example, "After I fed the cat, I brushed my clothes" compared to "I brushed my clothes after I fed the cat". But in German, there is a comma regardless of which clause comes first.
Also, interestingly, note what else they say. German doesn't insert commas where there is a pause like in English. So don't fall into that trap!
Yeah, you are right. But I think we get taught it in school because there are many, many uses of commas in English, many of which are too complex to be taught as a young child. For example, most people have never heard of the concept of non-coordinate/coordinate adjectives, but know to put a comma in "That is a large, heavy bag" but not in "That is a large steel building" simply because we tend to pause in the first one.
German has no such rules, there are much fewer reasons to use a comma than English.
That's a great way to think of it. 'wissen'=knowing facts, information; 'kennen'=knowing people, places, languages, being familiar with, etc. Think of the English terms we get from those two: 'wit' (a witty person knows so many clever things) and 'kin' (the people you know, your family).
When you're saying 'I don't know (or even if you do know)' in relationship to facts (what tomorrow's weather will be, if Jill is coming to the party, the difference between off-white and eggshell white when choosing paint colours...), then you want the verb 'wissen' (ich weiß (es) nicht). The verb 'kennen' generally refers to knowing people (related to the English word 'kin'): 'Ich kenne Herr Schmidt. Ich kenne Frau Schmidt nicht.).
In this particular phrase, 'whose son it is' is the fact that is known or unknown.
So to summarise: wissen = to know facts, information kennen = to know people, be acquainted/familiar with