is there a way in ArcGIS to save ModelBuilder (with all components) so that later on I can work on it?
There is 'save' in ModelBuilder but when I wan to import it to ModelBuilder it gives me all as one component instead of all original components.
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It sounds like you are either double clicking on the model in the toolbox, or dragging it into a new model.
To continue editing an existing model that you've saved, right click on it in the toolbox and choose 'Edit.'
I am not certain what you mean when you say you want to import ModelBuilder into ModelBuilder.
However, I think you should try a simple copy/paste of the contents of one model into another.