normal issue

Here is my UVW template.

I've put a bitmap with a uniform color on the whole mesh and also another uniform color bitmap as a normal map bitmap in the material... The objective is to get a kind of reflective aspect using a mobile/Bump Specular material (I'm targetting Android platforms). I'm a beginner in 3D game development and as far as I have understood, normal map are modifying pixel normals to get the influence of light changed, so if I'm using a uniform normal map texture, it should smooth the normal the same way isn't it?

I think he means with the mesh itself when he talks about the normals not your normal map, they are two different things. The mesh faces each have a normal which says which direction it is in. If one of these is facing the wrong way then you can get issues. Most std Unity shaders only display a face from one side, so if the normal is the wrong way you get a gap where the face should be. Some shaders do display both sides of a face but if one is facing one way and the one next to it is facing the other it can cause seams in the smooth shading of the model.

This might not be your issue but it is always worth a check whenever something is amiss.

The normal facing direction has nothing to do with UV mapping.

If your mesh normals are not facing the correct direction it will appear to have a see through gap. This is because the shader thinks we are viewing this object from the opposite angle.

A quick way to see this in action is to make a mesh and completely invert its normals. It will look like you are viewing the inside of your mesh, the closest normals to the camera being "transparent"

Follow the guide I linked to you. You most likely have to select your mesh and use the "Normal" modifier inside of 3dmax. Usually after applying the modifier it will fix itself instantly. If it doesnt you will need to select and flip the incorrect faces.

I think the misunderstanding is in terminology. In your question you state "So far, the normal map has a uniform color."

When people refer to a normal map they are referring to a map that controls the "bumpiness" or sometimes shininess of a mesh. Its sometimes called bump map.

The map you are referring to is the diffuse map. Anything to do with texture and color applied to a material. I just call it "the texture".

Your problem is with your mesh's face normals. The actual 3D object is causing this issue

I have noticed this issue pop up if I am breaking the model apart during UVmapping, mirroring the object, and sometimes during the extrude of a face. It is very simple to fix once you figure it out.

I have checked the mesh normals and I could not figure out how two connected elements could have their normals pointing to opposite directions... The mesh is correct and all the normals OK. Then, I've been looking around the UV and I've noticed that I had some flipped faces due to UV... I corrected this. If I use a specular material picked from Unity standard material library, I have a result which looks much more better...

But when I switch back to a mobile/Bumped Specular material, I still have this strange behavior at the tail boom transition area. So I think there should be a special technique with UV and normal map for getting a good result and I'm pretty sure the problem comes from the thing I'm missing while uwarping UVW and apply a normal map...

Can you get rid of this problem with any of the Unity import settings regarding normals and tangents(I know you said you did this but I wondered if you said it did not work because it messed up other aspects of your model), just want to double check?