Learn Russian: Напротив дома стоял неизвестный наследник. - Opposite the house stood an unknown heir.

In Russian, the end of the sentence is the 'rheme' or the place of focus, which introduces new information. By placing the subject at the end, it emphasizes that this is an unknown heir appearing on the scene, making it functionally similar to using the indefinite article 'an' in English. If the sentence started with Неизвестный наследник, it would sound more like 'The unknown heir (whom we were just talking about) stood opposite the house.'

Why is дома in the genitive case here?

The preposition напротив (opposite or across from) always requires the genitive case. Since дом is a masculine noun ending in a consonant, it takes the -а ending.

I sometimes see напротив used without a noun after it. Is it acting differently here?

Yes, here напротив is acting as a preposition because it dictates the case of the noun дома immediately following it. However, it can also be used as a standalone adverb meaning 'on the contrary' or 'across the street' (for example, Он живет напротив means 'He lives across the street').

Is the letter т pronounced in the word неизвестный?

No, the т in неизвестный is silent. It is a part of the root весть (news or message), but when combined into this adjective cluster (-стн-), the т drops out of pronunciation to make the word easier to say. You should pronounce it as if it were written 'неизвесный'.