Hi,
An exposto (male) or exposta (female) translates to exposed in English. Most researchers just leave it in Portuguese. For those who do translate it, most seem to use foundling.
She was given to a family for 7 years. At the age of 7, she could chose to remain the family or find another family to work for.
Some confession rolls exist. You'd have to go to the church and ask to see them and look through all the families for your ancestress.
The Olinda did arrive in NY on 2 Feb 1891. It was up to the captain to have EVERYONE on the ship counted in NY regardless of final destination OR just those disembarking were to be counted in NY and those going down to a smaller port (Boston, Providence, New Bedford) etc were to be counted at those ports. So you'd have to research the Olinda to find out if the ship sailed into other ports.
Cheri Mello
Listowner, Azores-Gen
Researching: São Miguel island: Vila Franca, Ponta Garca, Ribeira Quente, Ribeira das Tainhas, Achada