"There are people who do not have a house."
Translation:Es gibt Menschen, die kein Haus haben.
People, who... = Menschen/ Leute, die...
"Wem/Wen/Wer" are used for questions and are turned into "dem, den, der/die/das" if a statement is made. "Da" is used either with locations (= there) or if you there is logical causal construction like " Ich gebe ihr Geld, da /weil sie arm ist" = I give her money, as/because she is poor .
Yes, you are right: It depends on the article of the noun, in the simple version it is just repeated.
So it is Die Menschen, die..., Der Mann, der..., Das Wasser, das... or Akkusativ: Den Mann, den... and Dativ: Dem Mann, dem...
Later there are constructions like Der Hund, den du magst (der) bellt. (Der Hund bellt. Nominativ. Du magst den Hund. Akkusativ. But Den Hund, den du magst (den) streichelst du. Du magst den Hund. Du streichelst den Hund. Twice Akkusativ.
This special Grammar is for later, I think. For the moment it seems to be enough to repeat the article in relative clauses (see above).
I'd like to correct your sentence: Es gibt einen Mann (Akkusativ), der kein Haus hat (3. Person Singular). You can proof it, if you make two sentences: Es gibt einen Mann (Akkusativ). Ein Mann (Nominativ) hat kein Haus.
It is not easy to explain for a german native speaker. So I hope, I did not confuse you.
Ich gebe einer arm frau etwas geld.
"I give the poor woman some money"?
Is it correct?
Yes, number 3 is necessary when number 2 happens. "die" here further identifies the "Leute" in the first part of the sentence, so the second part "die kein Haus haben" is a dependent clause and you know from an older Duo lesson that the verb comes last in a dependent clause.
Here's a good article explaining it (German Subordinate Clauses at the bottom of the page): https://www.thoughtco.com/german-sentences-in-the-right-order-4068769
Late answer: ... who don't have a house is a relative clause, who refers to people and is called a relative pronoun. To translate the sentence you need a German relative pronoun that matchs with "Menschen", that is a nominative (subject case) plural here. Thus you can choose from die and welche.
Das is a relative pronoun for singular neuter, for example "Ich kenne ein Mädchen, das kein Haus hat".
Dass with the double s is a conjunction, it is used to begin a secondary clause, e.g. "Ich weiß, dass es Menschen gibt, die kein Haus haben". In English, "that" can be a relative pronoun, a conjunction and also a demonstrative pronoun. German has different words for that (conj. "dass", rel. pr. "der,die,das,dessen,dem,den,welcher,welche,welches,welchem,welchen", dem. pr. "der,die,das,dies,dieser,diese,dieses,jener,jene,jenes,jenem,jenen"), that are used depending on the word class, and for the pronouns the gender and the case (and the number) of the thing they refer to.
It is not really correct, it's rather something that children would say or someone in a very colloquial or low-level context. Correctly one would use a relative clause to describe or specify "Menschen" in greater detail. In a relative clause, the finite verb comes always last (die kein Haus haben). If you use the main-clause structure with the verb at the 2nd position instead (die haben kein Haus), you have two main clauses connected with a comma, which is a colloquial construction, as in correct German you can only connect to main clauses with a conjunction like und, aber, denn, ... Also "die" becomes a demonstrative pronoun in this construction, but it is considered colloquial or even impolite to refer to people/persons with the demonstratives der, die, das, e.g. "Der hat nicht mehr alle Tassen im Schrank" ~> "That [guy] is one short of a six pack".
You are right using accusativ after ohne, but Haus is neutrum (das/ein Haus - in nominativ and accusativ the same!) Es gibt Menschen ohne ein Haus.
Einen is the right masculine form, e.g.: Es gibt Menschen ohne einen Hund . (der/ein Hund - nom., den/einen Hund - acc.)
It will be still wrong, because Duolingo wants us to translate "There are people who do not have a house." do not have a = haben kein versus ohne = without.
lol, it shows proof you're a noob if you're looking at suggestions. never count on them unless it's showing you a noun or a verb or maybe an adjective. all the 'hints' aren't WRONG, they were just wrong in that SPECIFIC situation. in a different situation they might be correct.
No Leute is a plural noun like in english people. It is a number of persons. There is no singular word for it. For singular you have to help with one man/woman or in german ein Mann/eine Frau/ein Mensch.
In the sentence Leute is Akkusativ. For Dativ you are right with Leuten, but that would be a sentence like: Das Haus gehört den Leuten.