I'm glad you asked!
It has to do with the history and evolution of the Swedish language. A thousand years ago, Old Norse practiced the case system still found in German and Icelandic, having the four cases nominative, accusative, dative and genitive. In this system, the pronoun "han" was han/han/honom/hans respectively.
In medieval times, however, the Swedish language underwent changes and the case system was phased out. During these times, the original dative form honom somehow came to replace the older accusative han, and that's the way it happened to stick.
Curiously, you can sometimes hear sentences like "Jag såg han" in very informal spoken Swedish. Although this use of "han" as an object rather than subject is considered incorrect and strongly discouraged in writing, it's not just an error, but a remnant of what Swedish once was in ancient times!
Yes. It can imply romantic feelings/interest, which aren't yet as deep and strong as love.
Kinda amusing though, that this Swedish course is the first one in Duolingo so far where I've encountered a sentence implying a man having feelings for another man... Given that the Swede men have often had a reputation of, or have been a stereotype of a gay man. :D
[At least I've got that impression; no disrespect intended to gays, Swedes, or gay Swedes.]
I've heard it in jest from Finns, as Finnish are said to consider themselves more macho and tuff all around, and also in jest from northern Sweden about southern Sweden, and of course especially the capital ("fjollträsk"). The main difference seems to be that Finns and Swedish northerners are considered to be a laconic, silent bunch, while Swedes and especially Swedish southerners are considered more talkative (relatively speaking, I'm not comparing with Italians). There are a lot of jokes based on the strong, silent northerners and Finns. Anyway, as far as I understand it, this seems to be some very local, Swe-Fin one-upmanship, I've never heard that there should be such a reputation for real, and in other parts of the world. I'm curious, in/from which culture or cultures have you heard this reputation? :)
What is the degree of usage of the gender-neutral hän? Thanks in advance!