Yaaleh Viyavo When Davening
If you forgot to say Yaaleh Viyavo during Maariv and remembered after saying Hashem’s name at the end of the berachah, do not go back to repeat it.
If you forgot to say Yaaleh Viyavo during Shacharis or Minchah and remembered after saying Hashem’s name at the end of the berachah, finish the berachah and say it before Modim. If you already began saying Modim, go back to Retzei. If you already said the second Yihiyu leratzon at the end of Shemoneh Esrei, go back to the beginning of Shemoneh Esrei.
If you forgot to say Yaaleh Viyavo during Shacharis and only remembered after davening Musaf, do not repeat the Shemoneh Esrei of Shacharis.
If you forgot to say Yaaleh Viyavo during Minchah and only remembered at night, daven Maariv twice, once for Maariv and the second time as a voluntary tefillah. However, since it is no longer Rosh Chodesh, do not say Yaaleh Viyavo during either Shemoneh Esrei.
All the above also applies if you are unsure whether you have said Yaaleh Viyavo.
Hallel
If you are saying Hallel without a minyan, say the berachos at the beginning and end. When saying the berachah at the end of Hallel, the word al is omitted.
Many are accustomed to saying these berachos even when saying Hallel with a minyan. If doing so, say the berachos before or together with the chazzan, and do not answer amen on the chazzan’s berachah.
Repeat the possuk of Hodu after each of the three pessukim of Yomar na (even when saying Hallel without a minyan).
With regard to interrupting for devarim shebikdushah, Hallel shares the laws of birchos krias shema. (To elaborate: With Kaddish, you may interrupt for Yehei Shmei Rabba and the amen of da’amiran be’alma. With Kedushah, you may interrupt for Kadosh, Boruch, and Yimloch. With Modim, you may say the words Modim anachnu lach. You may interrupt for Borchu and for the amen of Hakel hakadosh, Shomei’a tefillah and birchos hatorah.)