I have an app that I like very much, I use it everyday, but I dislike its desktop icon.
How can I change the desktop icon of this app ? Should I do it directly by opening the .apk file (with which tool?) ?
You can try apk edit.
Note : This process will cause problem on update of the app.
When google play notifies the update, you can uninstall the app, install the app again and change the icon.
Most third-party launchers (home screen apps) let you replace an app's icon with one of your choose, and they feature downloadable icon packs: often with co-ordinated icons for common apps, so you can have all your app icons matching, or just change one you don't like. The exact method depends on which launcher you choose, so check out that launcher's help, or post a new question with the launcher you're using.
If you're mainly interested in changing the icon of a shortcut (not the icon in the app drawer), then you don't need to go to the hassle of installing and setting up a new launcher. Some apps let you create a home screen shortcut using any picture or icon of your choice, and choose what app to launch from this icon. For example, my app Showr (free download from Google Play) is a home screen widget with this feature. You can use a fixed icon that you pick from your phone or download, or you can even have the picture update from the web at set intervals (e.g. create a shortcut to the Facebook app with the latest photo from your timeline).
If you choose to do it this way, the steps are as follows.
You can change the size of the shortcut in the usual way, by long-tapping it and then dragging the handles that appear.