The widget simply reflects the task list from that view in the app. In other words, you need to hide completed tasks in the Inbox view in the app itself (see the screenshot). After that, the completed tasks will disappear from the widget as well (it may take a few seconds for the widget to get updated).
To make new items appear at the top, you need to modify the view in the app. Since there is no way to edit the predefined Inbox view, you need to create a new one. Or you can import the one I attached and see if it works for you.