When I try to change the width of a dashed line in Inkscape (from Fill and Stroke>Stroke Style), the program automatically makes all lines full, i.e. I lose the dashed style of the lines. Any suggestions on what I am doing wrong?
Change the width so that it doesn't become zero (or cleared). Zero width removes dashing. Insert some non-zero width and adjust it if you want to test what looks right in your drawing. Unfortunately the lengths of the dashes will change if the stroke width is adjusted, they cannot be selected independently.
There are more or less clunky workarounds such as "Pattern along Path", Object clipping and -masking or programming with code, but that's another story.
There are also other style factors which are bound with the stroke width - for ex. the markers. I do not know why Inkscape is built that way, but it's free and does also numerous things as expected - so no complaints here.