Learn German: Ich habe Angst, dass das morsche Dach der Ruine einstürzt. - I am afraid that the rotten roof of the ruin will collapse.

Because the definite article das is already doing the heavy lifting by showing the neuter gender. When a definite article precedes an adjective in the nominative case, the adjective takes the weak ending -e. If there were no article, it would take the strong ending and be morsches Dach.

How do we know der Ruine means 'of the ruin' here, rather than being in the dative case?

While der is the dative article for feminine nouns, it is also the genitive article. When a noun phrase like der Ruine directly follows another noun (das morsche Dach), it almost always acts as a genitive attribute showing possession or belonging. It translates directly to 'the roof of the ruin'.

The verb is einstürzen. Why isn't the separable prefix ein separated here?

Because the verb is inside a subordinate clause introduced by dass. In a regular main clause, the prefix would go to the end, as in Das Dach stürzt ein. But subordinate clauses push the conjugated verb to the very end of the sentence. When the verb meets its prefix at the end, they merge back into one word: einstürzt.

Could I use a different verb instead of Angst haben to sound more advanced at the B2 level?