I came first on earth but second on the heaven.
I also came twice in a week but found just once in a year.
I stay away from months but you can find me in February.
There are people and strange monkeys on this island, and you can not tell who is who (Edit: until you understand what they said - see below). They speak either only the truth or only lies.
Who are the following two guys?
A: B is a lying monkey. I am human.
B: A is telling the truth.
I am a word that begins with the letter “i.†If you add the letter “a†to me, I become a new word with a different meaning, but that sounds exactly the same. What word am I?