duplex numerus Romulo (dat) se ostendit

Latin Learning Latin
1

Priori Remo (dat) auspicium venisse dicitur: sex vultures; iamque nuntiato auspicio (neut. abl. sing.), duplex numerus Romulo (dat) se ostendit.

The omen came first to Remus: six vultures; and just then the news by an omen, twice the number made itself known to Romulus.

Do I have these cases (as indicated) right?

2

Yes, cases are correct.
Ita, recti sunt casus

iamque nuntiato auspicio no sooner had the omen been announced

3

Gratias tibi ago.

4

iamque nuntiato auspicio – this means “just as” or “right after the auspices were announced”