They end up together, and in one chapter, they go on a school trip together, where they look at the stars, and that is what the above page is referring to.
However, it's set in Japan, so that means that it is impossible for them to have seen the Southern Cross, a star constellation only visible from the Southern Hemisphere, hence the name.
Apart from that, I'll give a short recap of what's going on in the manga.
The Tsubakis finally had sex, and it really impacted on Tsubaki's test grade ranks. Needing to make up for it, she joins the sports festival committee, in order to get a recommendation letter. But she can only get the letter if her team wins!
Kyouta sabotages his own team to let hers win, as her grades dropping was somewhat his fault.
After this, Kyouta's birthday is coming up, and Tsubaki finally decides on buying him a 3D moon puzzle, because he loves the moon so much, but a woman asks her to let her take it for her son.
Through my clever fortune telling abilities, and the cliche past of manga, I'm pretty sure its safe to say that this new character is Kyouta's mummy.