And I'm still uncertain about the properties of utilons. What operations are defined for them? Comparison, probably, but what about addition? multiplicaton by a probability? Under which transformations they are invariant?

The same properties as of utility functions, I would assume. Which is to say, you can compare them, and take a weighted average over any probability measure, and also take a positive global affine transformation (ax+b where a>0). Generally speaking, any operation that's covariant under a positive affine transformation should be permitted.

Will you, then, say that a utility function which doesn't include everything is not a useful concept?

Yes, I think I agree. However, this is another implausible counterfactual, because the utility function is, as a concept, defined to include everything; it is the function that takes world-states and determines how much you value that world. And yes, it's very hand-wavy, because understanding what any individual human values is not meanginfully simpler than understanding human values overall, which is one of the Big Hard Problems. When we understand the latter, the former can become less hand-wavy.

It's no more abstract than is Bayes' Theorem; both are in principle easy to use and incredibly useful, and in practice require implausibly thorough information about the world, or else heavy approximation.

The utility function is generally considered to map to the real numbers, so utilons are real-valued and all appropriate transformations and operations are defined on them.