How did I get 2 libraries in Photos? How do I combine them?

• (Less important to me at this time) What did I do wrong to create two libraries instead of one that I wanted?

Most likely that you opened Photos with the external not available so it created a new library.

• How do I merge them and then get the Mac to search for duplicates?

You can import from one Library to the other (File -> Import) but the best way to merge is with PowerPhotos which does a much better job than the built-in procedure. Have a read of the relevant portion of its documentation

https://www.fatcatsoftware.com/powerphotos/VersionedDocs/v8/merge_libraries.html

and note that it can be set to manage duplicates as you merge.

https://www.fatcatsoftware.com/powerphotos/

Let me add to Yer_Man's comments that a big reason we use the trusted 3rd party app PowerPhotos ($40) is that it transfers albums and folders. Using Photos' own File>Import to bring in pictures from another Library imports only the pictures.

If you've put a lot of effort into organizing your pictures into albums and folders, then you will hate having to do it all again after the pictures get into the new Library, and PowerPhotos is the only solution. But if you have a Library in which there aren't many albums or folders, then using the free(!) method that Photos provides may work for you.

So you should check FatCatSoftware's links that Yer_Man provided.

If you use the Photos app to merge the libraries you'll lose all folders and projects in the imported library.

However, if you use the paid version of PowerPhotos you'll get the albums and projects as albums.

This is a comparison of the merge capabilities of PowerPhotos vs Photos:

I ran a number of tests with a 3119 photo, 72 video and 97 keyword Photos library with keywords, captions, keywords and locations.  I merged it into an empty library using Photos and PowerPhotos.  This is what I found was imported by each;

PowerPhotos:           Photos:

Albums***                                          -----------

Smart Albums (as regular albums)** -----------

Folders Containing Albums -----------

Captions                                             Captions

Titles                                                   Titles

Keywords* Keywords (some but not all: …

…see Note *)

Original images                                  Original images

Edited images                                     Edited images

---------------                                        Locations

Favorites                                             Favorites

Can detect and exclude                      Duplicates

duplicates upon import or not

Neither method could import/merge projects. 

Both methods could import older iPhoto libraries into a Photos library when the iPhoto library couldn't be migrated into a Photos library. 

Notes:

*The Photos app only imported 84 keywords our of 97. PowerPhotos merged 147 keywords. Photos only imported keywords that were embedded in the original file and not those added by Photos. PowerPhotos imported all of them.

**The original library had 90 Smart Albums. All were merged by PowerPhotos but, as indicated above, the Smart albums were brought over as regular albums. No album of any kind were imported by Photos. Also only PowerPhotos imported folders.

The original library had 34 regular albums and 1 folder with some nested albums. PowerPhotos merger all of them successfully.

The original library had 72 videos. Photos imported only 57. PowerPhoto got all 72 in its merge. In other tests Photos got all videos. All in all PowerPhotos is a much better candidate for merging libraries - in my opinion.