Agreed. Ayane loves Hayate as a brother, the same way Kasumi loves him as well. In the earlier games, this brotherly love to Hayate as well as her jealousy towards Kasumi was what made her Kasumi's rival in my opinion.
Hmm, here most opinions seems to be towards no, but on other places, the incest belief was stronger. I'm honestly not sure what to think, and this is a thing that will make me either main her or drop her entirely.
On the blunt side, you shouldn't drop a character based on character direction in resulting factors (unless there is valid reason that goes against you completely in regards to playstyle with a complete change all together). It hasn't even happened yet so I wouldn't go that further in progress.
Well, I think your "main" in a fighting game should be a character that you like completely right? Fight style, design, character archetype and so on? Having incestuous feelings, which may or may not have been shown in the franchise already is a big NO to me.