It is just a truncated form of ora.
óra¹ (tronc. ór) avv.
In your first example, it is used with meaning 2b from that link, i.e., as a generic link word to continue a story.
b. In principio di frase, ha spesso valore di congiunzione e serve a riprendere il filo del racconto o a passare a un’altra parte di questo
In your second example, as you already correctly assessed, or ora means just now.
I suggest you to add the Treccani dictionary to your list of go-to online references. A good monolingual dictionary is harder to read than a bilingual one, but often it is more detailed.