What do you mean by lose the texture, blender will export the coords for your model, but not the texture itself.

It depends on what you are exporting to. Are you trying to place it into a game engine or are you making a format that you plan on opening in antoher 3D program? In most cases, yes, the image should kept in the same folder as the exported model, but depending on what your final destination is there are different things that need to be done. Some game engines require you to name your material a certain way and link some empties to the object. Other 3D programs will require you to define a new material in that program, although the UV coordinates will usually travel over.

Scott