But I heard that Binance asks for a BTC10 or more listing fee from the developers or the founders of the project. If this is true, was there a time that Binance listed a cryptocurrency from the initiative of the owners of the exchange itself?
I believe this still happens from time to time. If they know the coin is going to give them money (in fees), has a strong community and it's not a confirmed shitcoin, they are probably going to support it.
E.g: I doubt Roger Ver had to pay anything for them to accept Bitcoin Cash. It was just an obvious choice.