They don't have the same etymology.
Ответ is the noun form of the perfective verb ответить; the verb exists in OCS as отъвѣщати, so it's pretty old and predates Slavic contact with the Germanic tribes.
Antwort is ent- (in Old German it was ant-) and Wort. So their similarity is coincidental. Sorry for going all detail with it but languages and word etymologies are my life.
If by that you mean prefix от- and prefix ent- share an IE etymon, and root ветить along with root Wort share another, then I'd disagree with that too.
От and ent- descend from different, albeit similar-sounding, PIE words.
The Russian cognate of German Wort (and English word) is "врать", to lie (it even shares the r!)
There is no cognate of German ent- which survived into any Slavic language according to my knowledge.
Is "на этот вопрос" in the nominative? Shouldn't it be in the prepositional?
It seems to be in the accusative case, for which вопрос would be the same as in the nominative. As to why - no idea. And I could very well be wrong.
It is Accusative case, and when you give an answer (or even just answer), you do it "to" a question.
The preposition на requires the accusative case according to a russion grammar. Pleasecheck.
Is this accusative or nominative? In Polish we user accusative in constructions like this, is it any alike?
It is accusative question, as you're giving an answer "to" the question. Think of it as a target of motion in this respect. With prepositional, it would be an answer "on" the question in a geospatial sense.
So we normally use prepositional case after на, For example "на столе" but in this example it's accusative because it's the target. Why ответ is not in genitive/accusative form? Я знаю ответа. Shouldn't it be кто знает ответа на этот вопрос
@MattinMaverick - Otvet is accusative, but inanimate (nonliving things) masculine nouns don't change ending in accusative case.