I'm happy to say that the outline of magnified (enlarged) sprites is now fixed. As that one took much more time to fix that I thought (since I've been on this point since several weeks now.), I'm quite happy to say that those white artefacts are now an old story.
For some odd reason, I wrongly thought it came from the coordinate system used for the map mode, and I've trying workarounds and fixes in that area for some time already, without realizing that the smoothing method (GL_LINEAR) was simply using the RGB values of the nearest transparent pixels, leading to those white and grey edges on sprites borders. Here is the result:
Might sound simple for some OpenGL experts out there, but I'm pretty glad to see this fixed.