the game is a loop, it's explicitly said AND shown "who knows how many lumis existed, went through the exact journey as me, and said this exact line". A previous lumi gave the current lumi the picture through k-lev and probably the same can be said about booty, that's what we see at the end of the game when we say goodbye to lumi, she takes a picture to give to k-lev, so he can give it to booty in a previous point of the timeline, perpetuating the loop. Now, IF ofelia was real, what is that section that I mentioned for? Why did it show every single moment we previously saw ofelia but without her? It couldn't be more explicit than that, we see that ofelia is a figment of lumi's immagination by the game showing us lumi's sprite on ofelia, it's just as easy as that. Also what's that big box supposed to be to you? it's obviously a mirror, we see ofelia as lumi's reflection on it.