When images are uploaded in Gallery, I noticed that it saves a copy of the original on the server if you have it set to resize to a smaller size. For example, the uploaded image is 3888x2592 and is 10.2MB in size. Gallery is set for the max image size to be 1600x1200, so it would be resized and have a much smaller file size. To save space on the server is ok to delete the original images that are stored, since they aren't used, or do they need to remain on the server for some reason?

The original image is used to rebuild all other images if you change the max or thumbnail sizes, and also if you add or remove a watermark.

They are always saved, so you would not be able to change the functionality to suit that specific need. As mentioned above, the originals are used when you change the parameters in some manner of how you want to show them on the front end, as a source in which to rebuild from.