Moving to a new computer - clarification please

1) Is Elements non-destructive like Lightroom, or do changes in Elements editor permanently change a photo, like Photoshop does?

Like Photoshop CC, Elements can use its ACR module to edit non-destructively. The parametric settings are stored in .xmp sidecar files for raw files and in the metadata header of the jpeg files. The normal use of the pixel editor is just like Photoshop.

2) Does the catalog backup include the actual physical photos? I've moved Lightroom between computers, and it gives me the option to include the physical photos when I export a catalog - Lightroom exports rather than backs up like Elements - I think it is the same thing.

The catalog backup, contrary to LR, stores not only the catalog (sqlite database plus accessory files and subfolders) but renamed copies of ALL media files.

Move Elements Organizer catalog

3) One issue is the person whose computer it is does not know for sure if all of her photos have been imported into Elements. Do you recommend I move the photos first, then backup the catalog from the old computer and restore it to the new computer?

I don't like the idea of copying the media files folder tree, then restoring the 'catalog', as a matter of fact, the folder tree of files indexed  in the catalog. I would perhaps do that before the restore process, but I would restore the cataloged files under a 'custom' master folder in the new computer. I'd create a folder directly under the chosen drive root (C: D: or...) so that you don't get overwriting.

4) Any other tips that I might not have thought of would be great!

You should be safe by using the backup and restore process. The 'reconnect' missing files process is not as simple as the LR one, so please play safe with that process.