Some of the wayward images may be in one of the other catalogues or a download to the external hard drive from the online backup (done last year).
Images are never stored in the catalog.
How can I merge the several catalogues, and should I?
There is no tool available to merge catalogs. The best you can do is to write the metadata to the files (File->Write Tags...) in each catalog, and then import all photos into a new catalog. In this process, you will lose albums and version sets and stacks and a few other things that I can't remember at this time. So, should you do this? If the drawbacks of the merge process don't make you say "Stop", then YES you should do this. I see no benefit, and huge amounts of confusion, caused by multiple catalogs, made even worse by the fact that they are overlapping.
How do I serch the the file in the external hard drive? I.e., how do I designate this file in the "browse" dialogue box for where to reconnect? I can navigate to it, but then what?
In PSE, you can find the name of the file, and this is the name you would use to search your hard disks using your operating system. Exactly how you do a search depends on your operating system, which you haven't mentioned.
I have windows 7.0 in a PC.
How can I see if the smaller catalogues have any photos that are not included in the largest? If they do, can I import these “extra” photos into the largest, and then ignore or delete the smaller catalogues?