I have all of other products, but I use them on weave hair which is 100% human. Can this product be use to style hair that is already dry?

I have used it many, many times on dry hair. I usually spray a little heat styler on the dry hair and then use it. In fact it works best if your hair is 95% dry or more . I would not use it I'm damp hair. It would take too long to dry.

is this product to be used on wet or dry hair?

Technically, it can be wet or dry hair to style. But it is a hair dryer. If you have alot of hair or heavy hair - I would let hair air dry till it is damp or dry a little first with regular blow dryer - then use this dryer. It does get hot but it does not blow as strong as a regular dryer, so it can take longer. Therefore damp hair is the answer. Also, for me I have used it on second day dirty hair as well just to straighten out a bit.

How does this compare to the Conair Infinity? They look exactly the same except for the coloring?

I own both. Honestly, I don't see any difference in the end result. The Babyliss Pro Nano looks like a more expensive and better made tool, and it should because it costs more. However, the Conair Infinity has a model that comes with both the 2" and 1.5" brush heads, while the Babyliss just has one nondetachable 2" brush head.