Well, my hotel has only 5 stars rooms but they only accept people logged in. Is that the way things work?

Well, you're the wizard.

Yeah. Anonymous visitors can only take 3-star or lower.

Anyone who clicks your proper link (you can find it, e.g., in my page), then s/he can gets your best room available, is it Economic room or a Royal suite... S/he needn't be logged in to do it. However, ASAIK my page can't be submitted to, e.g., Yarold's...