If you mean to tell the phone to show a picture of a closed folder instead of an open folder, no. If you mean logically close the directory (which is what a folder icon represents), that's taken care of in the kernel and you have no control over it, but it's usually closed the moment the OS is finished using it.1-Is there a way to tell a folder to close once I click a widget (and not only app)?
Yes. The normal way is to decompile the widget's apk file, change the icon picture file and recompile everything.2- Is there a way to change an icon of a widget?
All widgets are apps. I don't know what the "only" means - what else would you expect an app to be, other than an app?(some widgets are really "only" apps)