How do I export edited and starred photos to my hard drive?

Keeping your photos on an external hard drive is A-Ok. Now that I see your final statement I think I know what you are trying to do. You want to run Lightroom with the actual application on the Mac Book (as is normal). You also (apparently) want your catalog on the internal hard drive of the Mac Book, and currently you have your images, also on the internal drive, but you want to place them on an external drive, as your internal drive has only so much room.

Good news, more than one way to skin this cat.

The application, stays in the Internal drive.

Your catalog(s) can be on the internal drive, or an external drive. If you have more than one catalog, they do not have to be on the same drive or the same "place" (some of us have just one big huge catalog, some of us go for multiple catalogs, your call, pros and cons for both).

Your images, can be on the internal drive, or the external drive, and get this little extra, they do not have to be in thee same folder or sub folder under wherever your catalog is.

And as an extra extra Lightroom tip, they do not even have to be available to Lightroom much if the time, if you use smart previews (LR will use the smart previews) . Mind you they do need to be available occasionally (what I am getting here is if the images are not actually in the same place as your catalog, your database, and your previews, if they are on some external drive not connected to the Mac Book after import, if smart previews were created, then LR will still work (it will catch up to those files later). I am no the person to advise on this feature, never used it.

So, if you are preserving internal hard drive space you can do any of the following (mix and match)

Catalog on internal hard drive.

or

Catalog on external hard drive (could be slower)

Image files (RAW) on internal hard drive

or

Image files  on external hard drive.

and

Image files within file structure of catalog

or

image files somewhere else, say a separate folder on the external hard drive.

Some people will keep the catalog on their fastest internal drive, use smart previews, keep the images on an external hard drive, after import they might simply not attach that external hard drive (probably need another member to correct/clarify this), and have Lightroom use the smart previews, all for speed.

Now having said all that. If your intent is not to save exported copies of finished work., but to back up your work, then your question is all wrong. If you want a backup of your edits, then you need to backup the catalog, not just the images (previews can be ignored to save space, but I am not getting into that)

Step by step example.

1. Filtered on 4 star and above:

2. Selected those, then right clicked and started to navigate to export:

3. In the dialog screen that will come up, Selected where to export to:

4. Select the format:

5. And what ever other setting you want to change, And click on Export:

If you want copies of your images with all of the adjustments made using Lightroom, then you need to use the export dialog in Lightroom to export COPIES of your images. Lightroom does not modify the master images, it only stores the adjustments in the catalog. So in order to have an image file that contains all of the changes it's necessary for you to export a copy of that image using the Lightroom export functions.

How are you exporting. Are you doing that from within Lightroom using the export tool??

If you edited the photos and then removed them from Lightroom, your edits are gone and will have to be re-done.

If you didn't remove the photos from Lightroom, then your edits are still in Lightroom, just as you left them.

As far as exporting all your photos to an external HD ... why are you doing this? Most people don't.

To export photos and keep your edits and stars, you need to select Image Format as JPG or TIF. If you select "Original", you get the unedited and unchanged images.