Yes, but their total disbelief needs to be phrased in the correct form. Furthermore, not every exception will be valid. Altogether, it is a logical problem. They have to solve it correctly. I want to see their proposal in which they phrase their disbelief, because if phrased correctly, it will also be a statement of staunch belief in the exception that they propose.
Yes, but "I believe that all beliefs" is a belief statement. It is not a statement of disbelief. You are not really taking a risk. You need to say something like "I do not believe that any belief ..." Actually, to some extent you did. If we rephrase your statement in a form that takes at least some risk: "I do not believe that there exists a belief that does not stem from imagined experiences." So, from there, all we would need to discover is one such belief. The problem here is the definition for "imagined". When is an experience imagined and when not? Now, you need to take a risk by defining precisely the term "imagined".
Is a statement of disbelief a belief? I believe that all beliefs are false, except this one? I disbelieve all beliefs, except this disbelief? I disbelieve everything except I believe in the goodness of science? I disbelieve all hypotheses except for falsifiable ones with empirical evidence? I'm not clever enough for this.