In your first scenario - it SEEMS like the resolution is ALSO changing. This should not happen. if there are other check boxes on that page - experiment with them. when downsizing an image properly it should not be fuzzy.
For program 2
this does happen - make sure that when the photo is downsized YOU are looking at it on your computer screen at 100% visibility. Enlarge the window that the picture is in to be sure. an image of roughly 2500x1900 pixels reduced to 25% is VERY ROUGHLY 600 x 400. That image is definitely NOT tiny.
I would call either of the program's technical support line (if they have one) or google that program for specific info.
If anyone else can help...please do.
as an example this image is 550 x 305 pixels. The file size is 39.4 k
It's not the sharpest picture (but that has a lot to do with the chosen aperature on my camera during the shot) but I would not call it fuzzy.