Did you use DXTBmp or similar program?  If not, that right there is the problem.

Some textures in FS (specifically reflective textures) utilize a system called DXT3 with Alpha reflections to make the "chrome" or "bare metal" textures you see around, as well as the rest of the reflective textures.  Problem is, most paint programs can't read this material, so you end up painting something that doesn't work right on the model.  DXTBmp converts these files to something an editor can use, such as *.bmp files, and then converts them back again afterwards.

Download DXTBmp and fiddle around with it.  Also search through the posts in the past around here.  Every few pages there should be something along these lines.

Yep. It's normal practice to save the repainted texture in its original format. If this is not possible use a format compatible with the sim you're using.

PS. Most, if not all, the Alphasim freeware aircraft were originally created with AF99. Although some of the textures have been converted to BMP format they still retain their original .xAF file extensions. After saving from DXTBmp the textures might need manually renaming with their original file extensions before they will display.

Open the modified file in DXTBmp. From File/Save Extended Image save it in one of the 16 bit Extended formats under the original file name. I don't know which sim you're using but this would usually be in the same format as the original textures. For more info on FS texture formats read DXTBmp Help.