Is it possible to copy all of those photos in that desktop master photo folder to an external hard drive.
Yes, of course you can copy the photos.
I would then import a portion of those photos into lightroom on the laptop.
Importing photos is the wrong thing to do. Never import a photo a second time!
Or should i Export out the photos that I would like to edit on my laptop...make the edits...and then Import those newly edited photos back into the master folder on my I mac.
As with importing, exporting to move photos to another Lightroom is completely the wrong thing to do.
If I make changed to a photo on either machine, will they be recorded on the external hard drive...and will these changes be recognized by lightroom on my I mac when I plug in the external drive into it.
No, that's not how Lightroom works.
Since you have some misconceptions on this issue, please pay careful attention.
All of your work (edits, user-assigned metadata, slideshows, books, etc.) are stored in the Lightroom catalog file. It is this catalog file which must be made available to both computers on the external HD. By default, your work is not stored with the photos themselves (although optionally, you can choose to have SOME of your work stored with the photos). By using the same catalog file on both computers (since you have it on an external HD that can be moved back and forth), your edits are now available in the catalog file on both computers whenever the external HD is attached.
So this is the proper method. Using your operating system, copy the photos to the external HD, keeping the folder hierarchy the same. Also copy your catalog file to this external HD, put it in an otherwise empty new folder that you create just for this purpose. Then, double-click on the catalog file on your external HD to open the catalog file in Lightroom. You will then need to point Lightroom to the new location of the photos on the external HD. Right-click (Windows) or control-click (Mac) on that the level (parent) folder, select Update Folder Location, and then select the equivalent top level (parent) folder on the external HD. For more details, see "Part 2 — Updating Folder Location" of this document: Adobe Lightroom - Find moved or missing files and folders
Finally, I make these points again for emphasis: There is no importing in this procedure. There is no exporting in this procedure. Importing and exporting are not relevant to moving photos to another computer's Lightroom.