1) Yes. If they are embedded and external storage is NOT specified. If they are externally stored, you have an option to save a copy of the file where the images in the copy are not externally stored which you could then copy to your other computer.
2) Then your images likely will not be accessible until you update the file paths stored in the container fields to be valid from the context of the file's new location. You can actually use Replace Field Contents to update the file paths in container fields as though your container field is actually a text field, but you'll need how this data is formatted in your container fields. The actual text found there can vary with the insertion method used.
You may find this link that includes a download for a file that exposes this info in a field so that you can see it helpful: Exploring the use of a $Path Variable in Scripts
Thank you PhilModJunk,
I'll stick with embedding then!