Translation is quite a bit off...
P1: "Jun Asagi" said (Kouki) 勝ち逃げ君 = "(you are the one who) won and run away"
Means he had absent last year and Kouki won.
P4: Nao's Friend said え,弟って事 = "Eh, (Nao want to say that he is your) younger bros?" (Because Nao said that Kouki is not elder brother)
And the handwriting そここだわってるんだ = "So be fixated on (younger/elder bros issue)"
It's misunderstanding-pun.
What Nao wanna say is that Kouki = he is REALLY not blood relative.
What her friend understand is that Kouki = younger bros? (He was supposed to be elder twin)