Dear Rabbi I was just wondering about the following scenario. If some has started a meal before skiah (and didn’t daven mariv) on erev rosh chodesh and then benches after nacht, should he add Yaaleh Vayavo?

ב"ה Shalom If you have eaten after Tzet Hakochavim which ushers in Rosh Chodesh, Rosh Chodesh then requires you to say Ya'aleh Veyavo. However, if you have not yet davened mincha after shkiah, though you ate, the fact you haven't davened mincha shows that it is still a regular week day and you wouldn't say Ya'aleh Veyavo, even though the Tzibbur may have already davened Mariv. The issue becomes more complicated when Rosh Chodesh starts Motzaei Shabbat and he continued eating after Tzet Hakochavim. In this case the opinions in Halacha differ greatly, and therefore to avoid conflict one should finish eating Se'uda Shlishit earlier when he is required to say only Retzeh. (משנה ברורה תכד:ב, משנ"ב קפח:לג, מג"א קפ"ח, יח All the best