Would it be weird to name an American child with an Arabic name?

Nope. I love names that have meaning. I find that international names have more meaning than American names, like Delaney and McKenzie. Of your favorites, I like Demi (love) and Tatiana (so exotic) for girls and Kieran for a boy. If you really want an Arabic name, I love Zahara/Sahara for a girl (I prefer the "z" spelling though).