Should I delete APPLE HDD ST1000LM024 Media when selling my MAC

see this apple support page: What to do before you sell, give away, or trade in your Mac

that is the container that the macOS as well as the user's data resides. after you erase the drive and re-install macOS, DO NOT proceed with setup assistant. let the next owner do that.

see step 7 of the article again:

once you erase and re-install macOS you will always see "APPLE HDD ST1000LM024 Media" but your data will no longer be on the mac.

You can determine an internal disk by looking that at the picture below. When you delete the disk, all the data will be deleted and gone, so if you proceed to delete, the buyer should not have your data.

Unfortunately Apple's instructions assume you are using an SSD or the hard drive is encrypted using Filevault. Just using a simple erase on a hard drive still leaves your personal files accessible to someone using a data recovery app. I suggest you first enable Filevault on the system and let it complete the encryption process. This could easily take a couple of days.

Then while booted to a macOS installer launch Disk Utility and select the physical drive on the left pane of Disk Utility. Erase the physical drive as described in the Apple article. There is no need to unlock Filevault when selecting the physical drive to erase. If you don't first encrypt the hard drive, then you should instead write zeroes to the whole drive in order to destroy your personal files. If booting a macOS 10.13+ installer you will need to click "View" within Disk Utility and select "Show All Devices" so that the physical drive appears on the left pane of Disk Utility.

You can, but please make sure it is the correct internal disk and not anything else. Also make sure that there is no important data because it will format it completely.