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!
Ooh, interesting! A bit annoying given the wrong version is easier to remember though.
Thanks for this info! Do you have a specific source (web or a book) where I could read more about these things? :)
Not from the top of my head, but there should be some more info googleable. It might be in Swedish though.
I assume it would then follow that any corresponding mig/dig/oss/er själv could be substituted into that for "myself/yourself/ourselves/yourselves"?
Yes. Note that it's mig/dig själv but oss/er själva – and sig själv or sig själva depending on what it refers to.
Could this word imply romantic feelings or is there a different word(s) for that? EDIT: Durr, I forgot about alskar. Could it mean the same thing, though?
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.]
Sig själva is "themselves"
sig själv is "himself" or "herself" or "itself"
No, "thinks" or "is thinking" means "tänker" (tänk/tänka, tänker, tänkte/ har tänkt) It is not a synonym for "tycker om" (tycka om, tycker om, tyckte om) A synonym for "tycker om" is for example "gillar" (gilla, gillar, gillade/har gillat)