"jakého" (mladého, starého, nového... etc.) is the accusative masculine animate form. "Dům" is inanimate, so you need "jaký" here. There are sort of four genders in Czech. I don't quite understand the rest of your query.
Is the sentence structure in Czech like that? Like, putting the noun at the end of the sentence, or do they happen to put verbs at the end of the sentences, too. I'm wondering what's the most common thing to do.
We put at the end what we want to stress the most, what the new/key information is. Longer sentences have many possible word orders, each expressing something slightly different, unlike in English where the word order is very rigid.