Whether the alpha is 0 or 255 when the pixel is completely transparent, I don't know.
Yes, it matters if the dds file is normal map. It is actually ruining the texture.
When displaying the picture, it can not represent the transparent pixels. But that does not mean that R, G and B channels should be all set to 0. Alpha channel is separate from RGB channels, and they must not get altered with alpha.
The "other tool" is bug-infested allright, but that's beside the point.
It does not matter how the other tool represents the alpha channel. Actually, it completely ignores the alpha when previewing the picture and display RGB part only. That is why there is virtually no difference between wall01 and wall02, and that's how one can see that Paint.NET is actually destroying the RGB channels when resizing, and not during the actual editing.
I remind you that wall02.dds contains RGB channels intact WITH the srike of alpha across the picture. Wall03.dds is the outcome of resizing of wall02.dds. Not the eraser.