What is "Apple SSD Ap0512J media" and Container disk3 mean ?

By default Disk Utility now hides the majority of drive information from the user so it only displays "Macintosh HD" and "Macintosh HD - Data" volumes by default.

If you see all the other drive layout details such as physical drive, hidden Containers, and other APFS volumes, then it means someone clicked on "View" within Disk Utility and selected "Show All Devices". You can toggle back to the default by selecting the other option when clicking "View".

APFS stores data in "containers". The following Apple Support document explains some of the terminology and how it relates to volumes and partitions.

Add, delete or erase APFS volumes in Disk Utility on Mac - Apple Support

To expand on the article provided by John Galt, "Macintosh HD" is an APFS volume inside your main APFS container. (The main APFS container is usually disk3 on Apple silicon Macs). In your screenshot, your main APFS container appears to be empty, and contains no APFS volumes inside.

To resolve your issue, assuming that Disk Utility shows exactly the same as what your screenshot shows, select the APFS Container (Container disk3 in the sidebar), then click the (+) button to add a new APFS volume. Name it "Macintosh HD" and choose APFS as the format. Then, click Add. When done, "Macintosh HD" should appear slightly indented below the container entry, indicating that it resides inside that container.

Finally, quit Disk Utility, choose Install macOS when the list of utilities appears, and follow the onscreen instructions. You'll need a strong Internet connection for this.

encryptor5000--

While your suggestions of how to micro-manage APFS data structures are likely correct, one false move may leave your drive badly mangled. This is Not a recommended procedure for dealing with ordinary issues, and not appropriate for any but developer-types.

Most ordinary Users should ERASE the drive completely by its immutable manufacturer-given device-name, install MacOS from fundamental sources, and then use tools like Migration Assistant or Time Machine restore to replace their files.

¿What are you trying to accomplish there in the bowels of the structure of your drive?

There may be simpler ways to get what you desire.