Hi and welcome to Photoshop.
Let's look at the simplest example first - you want to open a raw file carry out some basic adjustments in Lightroom then open it and carry out some further edits in Photoshop.
To do that set your Preferences in Lightroom to Open in Photoshop as PSD or TIFF (your choice neither is better). Then after carrying out your Lightroom Edits just use Ctrl+E and the image will open in Photoshop. You can now add layers and carry out further edits etc. You can either use Save (to save to the original folder) or Save As to save it to a new location. Either way it will automatically be added to the LR catalogue. No need to import, although you may need to change the filters in the library module in order to see it , if you saved to a folder not in the original library filtering.
A variation on the above is Lightroom's Edit in Open as Smart Object in Photoshop. That opens the image as a smart object layer in Photoshop. Double clicking on that smart object allows you to open the content with camera raw and make further raw adjustments. When done just Save from camera raw and you are back in Photoshop when all adjustments are complete use Save or Save As as mentioned above.
You asked about Lightroom's Edit Original/Edit a Copy and Edit a Copy with Lightroom adjustments. You should only see these on non raw files. As an example, lets say you have a TIFF in the catalogue. Lightroom can make adjustments to that TIFF. If you then choose Edit in Photoshop it will ask
a. Do you want to open the original - i.e. open the TIFF in Photoshop without those Lightroom adjustments. This will open the TIFF in Photoshop without the Lightroom adjustments which you can edit. If you click Save in Photoshop, the Photoshop edits will appear in Lightroom on that original file, and the LR edits will be reapplied. Those LR adjustments can be readjusted if required.
b. Do you want to Edit a copy. This will open a copy in Photoshop without any LR adjustments. When you make your edits in Photoshop and Save then close, the Lightroom catalogue will have a copy of the file with the Photoshop adjustments and the LR edits will be re-applied. Those LR adjustments can be readjust if required. Because this is a copy, the original will also be in the catalogue.
c. Edit a copy with LR adjustments. In this case the LR adjustments are baked into a copy of the image which is then opened in Photoshop. After making your Photoshop adjustments click Save and close. In Lightroom you will have the extra copy in the catalogue with LR and Photoshop adjustments, but this time those LR adjustments cannot be removed or readjusted as they were baked into the copy that was sent to Photoshop. However, because this is a copy, the original TIFF also remains in your catalogue.
The best practice is to open within Lightroom as if you work independently in Photoshop then you would need to import the resulting files.
Dave