After accepting someone's Shared Album am I stuck with it until they delete it?
You can select the shared album in the sidebar, ctrl-click it, and then select "Unsubscribe". That will remove the album from your library.

Does this Shared Album of someone else's take up HD space or are they more like thumbnails? I am in the new Photos.
The shared photos are stored in your user library, in the size they are downloaded from iCloud. They are moderately sized image files, not larger than 2048 pixels wide. iCloud Photo Sharing FAQ - Apple Support
iCloud Photo Sharing supports JPEG, TIFF, PNG, and most RAW photo formats. When shared, photos taken with standard point-and-shoot cameras, SLR cameras, or iOS devices will have up to 2048 pixels on the long edge. Panoramic photos can be up to 5400 pixels wide.