tl;dr: “The femboy” (Nozomu) wanted both his sister (Nagomu) and the love of his life (Takushi) to be happy; so he tried to sacrifice his own happiness for them.
For Takushi, his happiness would come from marrying “Nazomu” (the “girl” he fell in love with back then); but he doesn’t know who is who, so he would’ve been fine with either one (prior to chapter 13) as long as they’re the girl. In chapter 13, Takushi realizes that he loves Nozomu, and wants to be granted permission to be with him, even if Nozomu isn’t the one originally betrothed to him (since the original agreement was to the daughter, Nagomu). Still, Takushi would’ve also been happy to marry only Nagomu since he loves them both (but only if that’s what they both truly want). The main obstacles to Takushi’s happiness are that he needs to be the heir/head of the Hatsujou to have permission to marry the daughter of Zenmai; and he’s only “allowed” to have 1 partner.
For Nagomu, her happiness would come from seeing her brother happy; but in chapter 13, she realized that she also loves Takushi, so marrying him would grant her happiness as well. Her obstacle is that only 1 person is supposed to marry Takushi.
[Questions 1, 2, 3] For Nozomu, his happiness would also come from marrying Takushi, whom he fell in love with in the past, and again in the present. However, he knows his sister also loves Takushi, and he thinks that marrying Takushi would be robbing her happiness. Additionally, Nozomu also has another obstacle: he’s expected to inherit the Zenmai business, otherwise his sister would need to take his place. And the one who inherits it wouldn’t be able to live as they please, so Nozomu doesn’t want to. Faced with an impossible decision, he chose to sacrifice his own happiness for his sister’s. He then went on to become the heir, implying that he’s completely given up on marrying Takushi, so that Nagomu would be his partner by default.
Still, that doesn’t mean Nozomu gave up completely. During the 3 years he was missing, he (presumably) worked hard and became manlier (you can fill in the gaps on “how”) in order to hold as much power as possible, as the head of the Zenmai. This way, he would be able to create that sci-fi Takushi clone, since he reasoned that having 2 Takushis would solve the problem of marriage. (Yes, the reason he had to reinvent himself and work so hard is just a gag; but his reason for becoming the heir is to free his sister so she can live the life she wants.)
[Question 4] As for why Nozomu planned to take over Hatsujou’s business: that never got addressed, but I assume it’s to free Takushi from his burdens as the Hatsujou head as well, so that he and Nagomu can live more freely.
Of course, in the end, Nozomu’s efforts were unnecessary, since neither of the other two wanted him to sacrifice his happiness, so they solved the aforementioned obstacles with polygamy (yay!)