I would like to add a delete icon (trashcan) in my actionbar. Is it a default icon can that an app can use or should the icon be a drawable in the app itself?
You can use
@android:drawable/ic_menu_delete in your menu XML. This will show the default delete icon across different versions of Android (meaning it will be different on different OS versions). If you want it to be consistent across all versions, you can also download icons from https://github.com/google/material-design-icons and include them in your project drawables folder.
I would very much recommend this icon pack from Google:
It includes their set of Material design icons.
This repository is extremely useful, with many Google / Custom icons: