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.