Lightroom to Flickr, can I delete originals from HD or will they be removed from Flickr too

If I delete the original photos from my computer (back them up to clear space on the computer) will they also delete in LR and then in Flickr? ... if for some reason, a year from now I decide not to subscribe to Lightroom anymore, would my flickr files disappear?

LR will remove a photo from Flickr under two conditions:

1. You remove the photo from the published collection and then click Publish.

2. You delete the photo from the catalog by doing Photo > Remove Photo (or typing Delete).  You'll be asked if you want to remove the photo from Flickr or leave it there:

Unless you do one of these actions, your photos will stay on Flickr regardless of what happens to your LR catalog or subscription.

The answer is simple, Lightroom operates and stores all the work you do with an image file in the Lightroom Catalog file.

Any time you delete the Original referenced file from your computer all the information with respect to that file will be removed from the Catalog. I.e Collections, Smart Collections, virtual copies, publish services, edits, metadata, etc, etc,etc.

When the info is removed from the published service it will eventually get removed from Flickr.

Are you using Lightroom Classic or Lightroom Cloud (CC)? Are you sharing Collections or Albums?

Yes, there are two ways to do this. You can drag the files in Lightroom to a location on an external disk. They will be moved over, or you can do it in Finder/explorer by say moving a folder of images. The images will get a question mark in Lightroom and you can simply point Lightroom to the new location and it will relink. Instructions here: https://www.lightroomqueen.com/move-photos-another-hard-drive-leaving-catalog/

>and if I unplug the external HD it won't affect my photos in flickr?

No they will all be fine.

I don't know the answer, because I have never tried to leave photos on Flickr while deleting them in LR. In fact, I consider this to be a very poor idea, deleting photos from Lightroom, that you otherwise want to keep.

If space is an issue, you would be much much much better off leaving the photos in Lightroom, and moving them to another disk. There are instructions on how to do this in this document: Adobe Lightroom - Find moved or missing files and folders

Also, since you use the phrase "back them up", Flickr is not a valid backup of your photos. Don't think about it that way, backups have to be exact copies of your orignals stored on a different physical disk. The photos on Flickr are not exact copies, they are exported JPGs, which are never exact copies of your originals.