I didn't see anything sexual between them; just two girls forming a friendship where there was only animosity before. You may be reading your own thoughts into it.
Fiamma is seeing Di as a pitiful creature that may simply need some understanding. Fiamma realises what's going on: Miss G has dropped Di as her pet and wants to adopt Fiamma as her new one, but Fiamma consistently rejects her, so Miss G takes her fury on others, especially Di. In turn, Di takes it out on Fiamma. If Fiamma can resist exposing Miss G as a fraud so much, maybe in turn Miss G won't be so hard on Di, and in turn, Di won't be so upset with Fiamma. In a place she doesn't belong, Fiamma is trying to make peace against dark forces.
I also sensed some sexual tension on Fiamma's end. The way she was looking at Di just seemed in a very endearing manner, which is odd considering their relationship up to that point. I didn't get the same sense of endearment from Di's end. She seemed content/happy with Fiamma, but wasn't looking at her adoringly or anything. It was just very odd to me. Maybe she realized when Di isn't trying so hard to impress and win the affections of Miss G she and Di get along very well. If there wasn't that level of competition from Di, maybe the two would be friends, and perhaps this is all Fiamma wants. Since Di is the biggest enemy of Fiamma throughout the film, it'd make sense that she felt happiness that they were finally getting along and she was finally receiving acceptance (even if short lived).
I think you are correct, it was entirely a friendship connection. Of course it was the most erotic scene in the film; especially with Di having the drawn on mustache. But I think any lesbian subtext is something supplied by each individual viewer, although deliberately manipulated by the editing and by what was happening in the other relationship.
The importance of the scene (and the reason they linger on it) is that it is at this point that a part of Fiamma's spirit becomes a part of Diana, which had symbolically happened earlier when Fiamma gave her the bottle. And Diana takes both with her when she leaves the island at the end.
I imagine there's not much else to stare at when someone is touching up your face, though I've never had it happen to me I don't know. That being said, I don't think there was anything 'romantic', 'sexual' etc. about this situation, just the girls prepping to have fun. They were growing in fondness, intimacy etc.
As others have said, when someone's putting make-up on your face, it's natural to look at her face.
Fiamma is shown watching the others several times. From the woods when they get out of flower-arranging class to go for a swim, right before she suggests they should compete against other diving teams, etc. She's trying to figure out her place among these alien girls in this alien environment.
I think Di applying Fiamma's make-up was a gift in return for the perfume and an acceptance of Fiamma's friendship.
I really loved that moment, because I think it gives us an insight into what Di and Fiamma's relationship might have been like had it not been for Miss G. being a constant source of conflict between them. I think after a bit of the initial friction that we saw at the start of the film, they probably would have been really good friends, and maybe even fallen in love as well. I definitely think there was a vibe of sorts in that scene. I hesitate to call it "tension" because I think it was more of an example of them being really relaxed with one another for the first time since they met.