Exporting catalogs from Lightroom Classic to Elements 2020

No, the catalog conversion only works from Elements to Lightroom, not the other way round...

So, I can think of two possible migration solution.

1 - continue for some time to use LR for organization (it will work without subscription) and using PSE instead as your external editor and raw converter to replace the development module.

2 - prepare your present library by 'writing metadata to files' (Ctrl S if I remember well), then import your library in a PSE catalog. That's the same as migrating to a third-party solution, but PSE has a serious advantage with raw files or even jpegs already edited in LR.

The ACR module in PSE has only the main editing features as LR or the full ACR in Photoshop; however PSE recognizes all parametric edits made in LR, even if it can only edit and change the main ones. You don't need to export tiffs/psd edited versions to take the edits into account.

It's easy to test it by yourself with a 30-days trial version.

Select a significant part of your media folders and write metadata to files (in xmp sidecar files or in metadata header).

Import those folders in a new catalog.

Another factor is interesting if you shoot raw: if you upgrade your camera, you'll upgrade the ACR module of PSE. That module uses the same sliders you are used to in LR, which should be more natural than working with third-party raw converters.

No it’s not possible. You can go from an Elements catalog to Lightroom but not the other way. Elements lacks many of the raw tools available in Lightroom Classic.

You could write metadata to files in Lightroom, export copies and add those to Organizer. Then choose to import the embedded keywords.