You have to be a legal resident to be able to access medical care in the same terms as a citizen. Have you looked into what you need for that already?
I'm a Swedish citizen, but I haven't lived there since I was a kid, and now I'm going back for my medical transition as well. I've been looking at the practical aspects of moving back there, and of course most of the information I run into is aimed at immigrants, so I can point you to some resources if you need that. Just PM me and we can talk about it over there.
The way healthcare works there is you pay for each visit to the doctor up to a cap (that isn't very high, really). The same for medicines.
For MtFs Sweden covers counseling, voice therapy, hormones, hair removal (I think it's electrolysis, since most Swedes are blonde and light skinned), BA and GCS. Another member from Sweden mentioned she just got FFS, but I don't know if she did it privately or if they're covering it now.
They require a year of RLE before any medical treatment, but they are getting very flexible with that as reported by the federation of LFBTQ people.
As for the legal gender and name change, I'm trying to find the sources I had found months ago, I can't remember exactly how it's done. I do remember it can be done without any medical treatment. I just found the text of a law that states you should have perceived being of the other gender for a long time, and having lived as your preferred gender for "a while". It doesn't say how long a while is, and they may have also gotten more flexible on this. I think I had read that the legal part was one of the first things I will be able to do once I set foot in Sweden, but I need to confirm that.
