The problem is that when i have to export it, and later I import it the textures are gone, the model appears black (like in the image) and the game that I want to export it to does not recognize the textures and they appear missing any solution (?)
It looks like you switched from Cycles render to Blender Internal render at some point (or maybe the other way around). When you import an OBJ, blender will automatically generate and assign materials to the models you imported, but the materials are generated only for whatever render engine you have selected when you import.
It looks like you imported the model with Cycles render enabled, then later switched to Blender Internal. Try just switching your render engine, then trying again, or redo the import/export process, making sure to keep your render engine the same.
I recognized this error because in one of your images, your material looks like some sort of sky texure-like thing, which is what happens when you switch engines and leave your materials the same.