In this sentence, "von" = "of": "Hans is the brother of Karl". ("Hans is Karl's brother" would actually be "Hans ist Karls Bruder".)
"aus" is basically "out of". (...apart from other meanings like "[turned] off" ("Der Computer ist aus"), but I guess you're referring to "von vs. aus" with regard to location?)
So, normally, to say that somebody/something comes from (i.e., lives in / was born in) a certain place (country, town etc.), you use "aus": "Hans kommt aus Frankfurt." (In some regions people might say "Hans kommt von Frankfurt", but that's not standard German.)
Accordingly, if somebody comes out of e.g. a house or a hole, it's "Er kommt aus dem Haus / dem Loch".
If somebody is coming "from somebody" or "from a meeting", you use "von": "Ich komme vom König" = I just came back from [a talk with] the King, or: the King is sending me [to give you a message]; "Ich komme vom Finanzamt" = I'm with the IRS [and want to talk to you about an issue with your taxes]; "Ich komme gerade von der Konferenz" = I've just been at / I'm coming from the conference. It can sometimes work in a geographical context as well: "Hans kommt von Frankfurt" = Hans is coming over from Frankfurt = the journey Hans is making in order to come here starts in Frankfurt.
The connotation of "von" is generally more about appropriation: "die Frauen aus Berlin" = "the women from Berlin", a group of women who happen to be from Berlin (but could well be somewhere else right now); "die Frauen von Berlin" = "the women of Berlin", the kind of women (collectively speaking) who are typical of Berlin, and an integral part of Berlin (and who are very likely in Berlin right now).
So what you'd usually say is, for example, "der Käse aus Frankreich" (cheese that comes from France, not cheese that "belongs to" France), and "die Wälder/Burgen von Deutschland" (forests/castles don't come from a country, they "belong" to it, because they can't move away) - or better yet, "die Wälder/Burgen Deutschlands", because "von [+ dative]" is, again, really just a substitute for the genitive (like "Bruder von Karl" - "Karls Bruder").
Hope this helps?
No apostrophe: "Karls Bruder". Apart from that, it's correct.
There's no apostrophe to indicate genitive in German, only to show where a letter (or several) is left out: "Wie geht's dir?" = "Wie geht es dir?"
In Germany you sometimes see apostrophes e.g. in names of small businesses, but that's wrong; e.g. "Anna's kleine Kneipe" instead of "Annas kleine Kneipe" ("Anna's Little Pub"). Don't let them confuse you. They're called "fool's apostrophe" ("Deppenapostroph") for a reason. ;-)
I'm not sure why Duolingo teaches you the colloquial way of saying this (with dative case, like "der Hund von dem Mann" = the dog of the man). The standard way is simply the genitive: "Hans ist Karls Bruder" = "Hans is Karl's brother"; "der Hund des Mannes" = "the man's dog".
Being in a dative lesson doesn't mean all nouns you see are going to be dative. "Der Bruder" is nominative because you always use a nominative object with the verb "sein." There is a dative noun here though-- it's "Karl," since the preposition "von" takes a dative object; there's just nothing special to mark "Karl" as dative since it has no article.
please Duo, its possible to do something with that still repeating of the same sentences in practicing of lessons in the level five? Because its crazy to still repeating that Hans is Kalr´s borther, or Eggs with chesse and Pants with flowers. All lesson til tle level five was good, but that practice is boring, really. Use more examples please.