Regarding this sentence:
Du hast immer Fragen gestellt und darauf bestanden, dass ich antworte.
I’m really confused because intuitively I would say that dass is right, but it doesn’t really initiate the subordinate clause, does it?
It may sound surprising, but the subclause marked by dass can in fact be governed by verb, a noun or a substituting pronoun.
Most common form:
Ich verlange, dass du mir antwortest!
Subclause governed by noun:
Die Vorstellung, dass ich dir antworte, ist abwegig.
Subclause governed by pronoun:
Ich bestehe darauf, dass du mir antwortest!
The set of pronouns that work like this is small and closed, and they tend to be compounds of da-.
It is correct.
If it were das instead, what word would be targeted by the article/pronoun?
I don’t really see your problem, but of course there is a subordinate clause and it is initiated by dass. You can tell that it is one because:
if you extend it with an object, you realise that the verb is last:
[…] dass ich dir antworte.
And it has to be dass (and not das) for a variety of reasons, including:
There is no neuter word that is directly referenced. Compare:
Das Wort, das ich dir sage, ist die Antwort.
It can stand all on its own which is not possible for relative clauses starting with das:
Was verlange ich?
Dass ich dir antworte.Was ist mit dem Wort?
Das ich dir sage.
Das Wort, das ich dir sage, ist die Antwort.
It cannot be replaced by welches (which is an almost certain indicator for das and not dass):
Du bestehst darauf, welches ich dir antworte.