How to make a transparent 'png' image from black (not transparent) to nothing (absolutely transparent) in GIMP smoothly?
As result, this image on the red image gives the image from black via dark red to red?
This is an example (but not of good quality, I'd like to know how to make this image properly):
What you are looking for is a gradient.
Here is a tutorial on how to make a gradient in Gimp.
Here's on how to make a custom gradient.
In your case you would make your gradient as a layer that like you said smooths from black to nothing, this will be your gradient layer. The layer under this will simply be filled in red. With the gradient on top it will make the effect that you want.
Alternatively you could just have a layer of a custom gradient that goes from black to red.
Hope this helps. :)