It is said that nihilists don't believe in anything, including nihilism.

Yes it is possible. It’s called knowledge. Knowledge goes beyond belief because it is what you gain from. Beliefs are often created in the subconscious mind and can be guess work rather than get to know the facts about something. Gaining knowledge in facts is realistic. I don’t believe or disbelieve in anything. I prefer to gain knowledge in facts and what I see in front of my own eyes by seeing things as they really are instead of being involved with the subconscious mind. Knowledge comes from the conscious mind while belief is guess work which can either be right or wrong.

Everyone who is capable of belief...believes many things, probably hundreds or even thousands of things. *** Consider: even the meaning of words, even the value of money, even one's own name and parentage, are all things taken on faith, the typical person never observing logically-conclusive proof of such things. *** The very act of you asking this question demonstrates that you believe that the words you are using have meaning, and that others will understand that meaning. When you were writing it, you could not be sure that anyone else would understand what you meant, that anyone else would read the words, or that anyone else would respond. You believe the words have meaning, you believe that others recognize those words as having the same meaning that you believe that they have, and you believe that others will read and understand and reply appropriately. *** And what if I am not one of those people? What if I misunderstand every word in your question, and all of the words in my answer are intended to have meanings very different from what you believe they mean? In that case, even though my answer seems relevant, it might not be. You believe that it is relevant, because the words have meanings that are relevant...or so you believe.