Firstly, I must say this is an extremely interesting case, and the sleuthing done on it thus far is amazing! Some of the items I am pondering:
1) Elfrieda is burned on the back of her head, arms, legs (limbs), and feet. While I am leaning toward electrocution of some sort, I have to wonder if after the guilty parties (and I think there is more than 1) electrocuted/beat her, they were trying to rid themselves of her body so she could not be identified. Maybe they attempted to stuff her in the furnace for burning but were unable to do so - one time trying to push her in feet first, another head first and/or raising her arms to go through with head - this would account for the arms to be burned (first part of the body to enter the furnace), but only a limited amount on the head (couldn't get her shoulders in).
2) Barney's behavior would be consistent with a person who, if he wasn't directly involved, knew there would be a problem for a friend/co-worker/etc. when Elfrieda was found - especially found at the police station. You don't want to implicate someone but you certainly cannot cover up someone else's crime. On the other hand, if Barney was involved, his odd behavior would also be consistent with someone who is trying to "act" the part of being shocked and surprised at the finding of Elfrieda but who actually knows what did happen and he had a role in it. None of the suspects are professional killers (as far as we know) so I cannot imagine this would be easy to pull off.
As for the letter....I am of the belief that there was something more than just friendship being alluded to....however, if you read written correspondence from days of old, there was a more romanticized feel to them even between the same sexes where there was no established same-sex feelings. Letter writing was quite an art and very expressive.
Poor Elfrieda was definitely murdered in my opinion.....it is the who, how many, etc. that I keep going back and forth on. I do not think it was highly premeditated - I think it may have been thought about and the timing of the opportunity presented itself that evening - hence, the chaos surrounding the clues left, the behavior of certain people, etc. I think there were others - not directly involved in killing her - who knew who was guilty also - including Elfrieda's friend. I think she might have took off - scared or was brought somewhere to keep tabs on her. When it was known the police were looking for her to question, she returned - but had her "story" by that time.
If Elfrieda really did think she was going to survive her ordeal in hospital (one quote was made that she was sure she would get well), she might have thought it would benefit her (for what, I am not sure) if she kept to her self-mutilation story. I have to really wonder how coherent she really was during those last few days in hospital and how much was made up (to sell papers) or words were put in her mouth by people who really did love her and thought they were getting certain responses to questions.
Just some thoughts - Creole