Could nabi buy the site: Yes, but no. Unless hagan has plans and wants the "$" for the site it is unlikely.

Can the devs incorporate it in the forum/game: Yes, it is possible, just as is possible to view the sets from the site. With hagan's help the developers could easily set up a page or functionality.

Would it be a problem with storage space over time: Depends, considering the textures are hosted on the Toribash texture's website (unless i'm wrong and their hosted somewhere else), it could potentially if it gets enough uploads, however, considering Nabi controls servers and things and stuff already, it could potentially be manageable.

It would be a good idea, however it truly depends on Hagan's choices since he developed the site.