A second question: does your theory allows distinguishing between "cuteness" reaction and nurturing/baby-raising protective behavior?

Mine doesn't. I think that instinctual mechanisms for "nurturing/baby-raising protective behavior" is a really big deal for mammals, so much so that the mechanisms have a tendency to be overly robust. (E.g., some men lactate.) However, I would defer to an expert on this, and would ask one (read a book) if something rested upon the question.

please give examples of non-primate mammalian behaviors that indicate the animal found an animal of a different species "cute".

I look forward to the day when we can scan an animal brain and see what they think and feel. Till then, I can't comment on whether animals think their babies are 'cute'. There's no doubt though that nurturing/baby-raising protective behavior is triggered across species. However it seems context-dependent: the parenting animal must have reason to consider the baby part of the family. So domesticated animals are likely to show this behavior to other pets and babies. (My cat tried to teach my first baby how to hunt when she started crawling, but didn't bother with the second.) Birds will take care of other birds if they're in the nest, etc. And of course there's Tarzan, which might have been based on some kind of observation of this kind.