re: Is there a way to crop homescreen widgets?
As far as I know, no launchers currently on the Play Store offer control over how widgets adapt to being resized. Launchers can do things like scaling and rotating of items on the homescreen (Lightning Launcher does this, for example) but I do not believe they can control the layout within an individual AppWidget:
The "provider" is a part of the same app that has the widget in question (i.e. Google Keep). This specifies the behavior of the widget, which includes any necessary layout work. The launcher (i.e. Nova Launcher) acts as the "host." It is able to embed other apps' AppWidgets inside itself, but cannot directly control them. Unfortunately, I couldn't find any other launchers or modifications (such as an Xposed module) that would allow you to do this.
The behavior of an app widget is published by an "app widget provider." An "app widget host" is a component that can contain app widgets (such as the home screen).