Photos Shared Albums

"First, are the photos actually resident on my computer?"

After you import the photos from the Shared Album, they are resident in your Library. The extent they are resident on your computer depends on other settings unrelated to their origin.

"Second, when they were imported did Photos import a full resolution image?"

The photos are imported at the resolution stored in the Shared Album, but Shared Albums have a lower maximum resolution than modern cameras. (Shared Album photos are limited to 2,048 pixels on the long side.)

"Finally, if I "unsubscribe" to the shared album or the owner deleted the album or any of its photos, would the images be deleted from my computer, and if so how could I prevent that from happening."

Once imported to your Library, the photos should stay there even if you lose access to the Shared Album or the photos therein.

Mark already explained what will happen with photos that you import and save to your library.

An add-on to explain how the Shared Albums are stored in iCloud:

• Shared albums are stored in iCloud, using a free part of iCloud, that does not count against your iCloud subscription.
• When you subscribe to a shared album, the photos are shown in your Photos Library, but not stored in your Photos Library as imported images. There is just a cache in the library package, where they are downloaded to (on my Mac with Sonoma I am seeing the cache here: ~/Pictures/Fotomediathek.photoslibrary/scopes in the subfolders cloudsharing and derivatives).
• This local cache mirrors the shared album in iCloud and will continually be updated, when someone adds new photos to the shared album, and photos may vanish, when the person who shared the photo deletes it from the shared album. Then the shared photo will be deleted from iCloud and the next time you reset your shared albums and they need updating from iCloud the shared album will no longer show the deleted photos.

It is essential to save any shared photo you want to keep by importing them from the shared album, as soon as possible, so you will have access to them, when they have been removed from the shared album in iCloud.