Alaikumassalam wa rahmatullah,
For Areesha please look at this answer: Information on 1, Anabia 2, Areesha 3, Ashna 4, Suha 5, Minha
Anooshay, which can also be pronounced as Anoosheh, Anoosha, Onusha, Onusheh, is a Farsi word that means eternal life, immortality, goodness and happiness, "bravo", and blessings of Allah. It is not an Arabic or Quranic word, but since the meaning is good you can use it as a name. It seems to be used only for girls.
Anooshay has many different correct pronunciations. You can begin it with a short "a" as in (U)ltimate or a long "a" as in (A)rdent, or with an "O" sound as in (O)mar.
It is the name of a famous Iranian woman, Anousheh Ansari, who was the first Iranian to fly to space.