It's very exciting to hear that you are planning a trip to Ireland in March.
With regards to your first query, you are correct in saying that all airline passengers
to the United States ages two years and older, regardless of vaccination status or citizenship, must provide a negative COVID-19 viral test taken within one calendar day of travel. There are many private companies in Ireland providing PRC tests where you can receive the document required to travel.
Secondly, if you are planning to travel to both the Republic of Ireland
and Northern Ireland
during your trip, I would simply advise you to ensure that you meet the entry requirements for both countries.
I hope this information will be helpful to you.