I believe that most of this can be resolved without typology. Where typology comes in, typology serves as kind of a map saying "you are here" and a rough sketch of the terrain. So with Fe vs Fi, it's the same terrain, but Fe is where you start and Fi is where other people start (or vice versa).
What you're doing here is mapping out the terrain. You're starting with those things obvious to Fe, and progressing to those things more obvious to Fi. In particular, Fe types tend to lack a degree of emotional "self-awareness". That isn't a "lack of feeling", but a lack of how internal processes affect feeling. Fe types think in terms of external processes affecting feelings, and deal with feelings in terms of those externalities. That's the scrap of the map of human emotions that Fe types start out with.
There's nothing wrong with this starting point, just as there is nothing with its introspective opposite, focusing so much on self-awareness that while an Fi type can be highly aware of others' emotions, the "Fi map" maps these all back to the introspective paths with which they're familiar. It's not in terms of Fe externalities.
I had an INFJ friend telling me about her dealings with an INFP friend who is helping her deal with some difficult emotional stuff. Aside from chatting and just being a friend, the INFP took my INFJ friend to a meditation session that she found very helpful. The INFP is effectively lending her the Fi half of the map, helping her with the introspective side of things.
As far as "selflessness" goes, I see both Fi and Fe types go overboard on being "selfless", and see no reason to attach the phenomenon you observe to a particular function. They do it for very different reasons. The Fe types do it typically because they lack that internal sense of self-awareness to maintain boundaries. The Fi types, on the other hand, should be totally aware of their boundaries (and they are, sort of), but deliberately allow them to be violated because of "love". Superficially, the behavior is kind of the same. Internally, the psychological landscape is different (different parts of the same "map", to continue my map metaphor).