Ubuntu – In a .desktop file, what is the “%U” variable

You cannot set the CWD inside a .desktop file. If you want an application to have a specific CWD, you will need to write a simple wrapper script for the application, that looks something like this:

#!/bin/sh

(cd /where/you/want/it/to/be && exec your_program)

You can replace your_program there with $@ and run the script with your_program as an argument, like run-in-dir.sh your_program. This way you can use the same script to wrap any program you want to start in that directory.

It's dependent on the icon theme. If the icon is not given by an absolute path, following rules are used to find the icon:

The lookup is done first in the current theme, and then recursively in each of the current theme's parents, and finally in the default theme called "hicolor" (implementations may add more default themes before "hicolor", but "hicolor" must be last). As soon as there is an icon of any size that matches in a theme, the search is stopped.

[...]

The lookup inside a theme is done in three phases. First all the directories are scanned for an exact match, e.g. one where the allowed size of the icon files match what was looked up. Then all the directories are scanned for any icon that matches the name. If that fails we finally fall back on unthemed icons. If we fail to find any icon at all it is up to the application to pick a good fallback, as the correct choice depends on the context.

See the Icon Theme Specification for details.