As Robert has said, right now images and processing histories must be saved separately, using image files and icon files (XPSM files).
This is going to change completely with the new project functionality, which I'm working on right now. It will be available (a first version of it) in PI version 1.7.0. Basically, a project file will be able to store all of your images with their histories (including undo/redo states), icons, workspaces, tool settings, preferences, color management settings, RGBWS settings, ... a lot of things
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There is something important that must be pointed out regarding your second question. When you create a new image with any tool, the process instance that originated the image is always stored as the image's initial state. You can access the initial state from the History Explorer window. Initial states are always ProcessContainer instances that store the sequence of instances that have been executed to generate an image. For example, you can try the following procedure:
- Open any image.
- Apply any sequence of processes to it.
- Right-click the image and select the 'Load History Explorer' context menu option. This will open the History Explorer window to show the image's processing history, where you have all processes you've applied in the previous step.
- Now click the image's main view selector (the vertical tab at the image's left border) and drag it to the workspace. This will create a duplicate of the image.
- Right-click the duplicate image and select 'Load History Explorer' again. On the History Explorer window, expand the <Initial State> item and you'll see the same processes that you applied in the second step. This is the initial state of the duplicate image.
An initial state represents the 'baseline' form of an image in PixInsight. Unlike the rest of history items, you cannot undo an initial state. When you drag the blue triangle from the History Explorer window, the initial state is not included in the resulting ProcessContainer. You can however click and drag the <Initial State> item to create a ProcessContainer icon.