Some applications, specially some running under Wine as the one in the screenshot above, show their icons in lower resolutions than the original, and I'd like them to show the icons in full resolution or to be able to change the shown icon. Does anyone knows how to do that? By the way, I'm using Latte Dock and its built-in task manager.

I do not know how to handle wine-applications, because I never used it. Normally, you can set the option Icon= in the corresponding .desktop-file in /usr/share/applications (systemwide) or ~/.locale/share/applications/ (per user). If the icons are in the default location you do not need to provide a full path.