Hachi had a series of tweets about anagrams before coming up with "Rangge Poppel." It is definitely meant to be an anagram of "doppelganger," even if it's one letter off for whatever reason.
Sylvia***** and Rangge are always shown side by side in the video until a bouquet covers the place where they used to be connected. So, yeah, they're conjoined twins.
When they sit down, they each have to keep pulling the chair toward them. (Musical chairs in Japanese is literally "chair-taking game," notably.) So that "game" ending would mean that each could sit down without issue and "be happy."
Any time a word (or line, even) is doubled, it seems to be a case where it doesn't really matter which of the two is being talked about/is talking. Sorta not sure about this.
The contract would probably have something to do with their separation surgery. I dunno, it might be symbolic or something, despite it being rather specific that it's a written contract on parchment.
When Sylvia is talking about giving Rangge a bouquet and Rangge refuses to listen, it's probably symbolic of their surgery (since the wound looks like a rose and all), and Rangge looks like she'll break if touched because... well, she does.
A few people have also suggested the bouquet representing their heart, which, if there's only one, gives a definite reason why one has to die. Although if they actually knew this was the case beforehand, I'm guessing they wouldn't have gone through with it.
Apparently, while they both seemed to agree they'd want the "game" to end at first, when they get the opportunity to do so with the "contract," Sylvia is glad to give Rangge flowers (perform the surgery), but Rangge knows what might and does happen.
This would certainly explain what Sylvia has to be sorry about in the ending... except that's not present in the Japanese text. Cough.
I know this is supposed to be MY analysis, but here's a question for you - why does Sylvia look so darn happy in the "in this world" part? Great job holding onto that bouquet and living, you unnamed jerk.
After "even like this, even like this," it might be saying "nemure," telling Rangge to "sleep." But even Nico was trying to guess what it is ("Lemonaaade..."), so it might not be that clear.
When Rangge is dying, she/both realize how stupid it was that she basically died just because they wanted to sit in chairs properly.
Saying "there's only one" is likely short for "there's only one of us now." Aww.
As for who's singing, I think it goes like this. The first part is probably both, since their voices always "become one." Also, when they're telling each other "yeah, don't need YOU anymore!", they, um, desync.
At "the truth is, it's lonely," it switches to just Sylvia, since she's left alone in the end. Rangge obviously has "only a little voice left," so that's her. Last chorus could be both, and the last parts are Sylvia (though I'm sure the second "goodbye" is meant to be Rangge's).
***** My mostly arbitrary name for the girl who survives, always standing on the viewer's left. Nicopedia calls them "left girl" and "right girl," so you can mentally replace Sylvia with "Langge" if you wish.