Humaira means "little red thing" literally, but it is used to mean "little white thing". The Prophet used to call Aisha Humaira sometimes as a loving nickname. As for humair, it could have the same meaning. Lisan al-Arab (the most respected Arabic dictionary) says "it is a name" and doesn't give any other information.
Note that Humaira shouldn't be written as Humairah (with an "h" at the end). Many female names can be written with or without an "h" at the end, but Humaira, like Hamda, never has an "h" at the end.
As for Unair, I couldn't find in the dictionary. I found a number of forums online that said the word أنير (which can be read as both anir and unair) is from a non-Arab race and has no meaning.