is a conjunction and praetereā
an adverb, so it can't be "after which things" and "besides this one thing" as they would be respectively rendered with prepositions: post quae/haec
and praeter hoc unum
goes with the verb: "After he had said these [words/things] ..."
Your first translation of the second sentence was correct. As you guessed, monēre
can take a double accusative. In his Latin primer, Kennedy says (208, Note 3.):
moneō, advise, accūsō, arguō, accuse, cōgō, compel, take Acc. of the Thing if it is a Neuter Pronoun:
Hoc tē moneō: I give you this advice.