You do not have to pay a fee.

Thanks a lot, audiokid! I hope your information is reliable. Actually how exactly do you know that? I'd like to be more informed about those things.

Time ago I wrote a letter to Yamaha asking them the same, and they replied, but I was not sure what exactly they mean. My impression was that they have given me only the right to play the piano home, but if I was to sell a recording then I probably had to pay for some additional license. Then I asked them again, being quite concrete, but they never replied to my following letters.
Of course I am quite disappointed by Yamaha for not replying me and not giving me a clear answer and I doubt that I would buy any other Yamaha product. In fact I'd supose that it could be that I have given them a very bad idea, but...

Just in case, here is the Yamaha's reply:

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Hello,

Thank you for contacting Yamaha. The demos in all Yamaha products are copyrighted and may not be used for anything other than demonstrating the features of the product. All other Yamaha original content, including, but not limited to, Voices, Styles, Patterns, Multipad data, and any other original content created by Yamaha, is copyrighted. If you are using the instrument to create your own original work, we applaud you... you have Yamaha’s permission to use the content (other than demos) for this purpose. If your intention is to copy our intellectual property and offer it for free or for sale, that would be an infringement. Permission will not be granted for this purpose under any circumstances.

Regards,
Yamaha Customer Support

I'm assuming you aren't using their demo songs are whatever loops they are using to demonstrate their product ( exactly)? If you are using the keyboard and its patches like any instrument, you do not have to pay royalties.

This is why you "bought it". You own the piano and have the rights to use the voices for making music. Its exactly what they replied to you in my words.

Go for it!

Absolutely, I don't use any of their demos. And I asked them concretely about selling music created and played by me.
I am confused by their insisting that not only their demos are copyrighted (and provided only for demonstration use and not for sale), but also "All other Yamaha original content", i.e. their voices, styles, etc are copyrighted (which may very well imply that they may only be used to "play at home", but not sell what you play/record).

Still, how do you know all that? I also thought the same ("I bought it, after all"), but one never knows. Well, perhaps I should not stare too much at that, but I really don't want legal troubles.