Easiest way to move library to new PC

What is the best way to move Callibre library and keep HDDs synced?

Old PC Windows 10 - "export" Callibre library to external HDD. 5 files.

HDD - "Import" Callibre library to new Windows 11 laptop. All books are there.

Then, I purchased some books from B&N when I found a 10 year old B&N gift card. The new books are now in my Calibre library on my OLD PC since it had the old Nook app on it. They are not on my new laptop yet.

Now, I have some questions:

1. Can I use Export on Callibre to export ONLY those NEW books to the HDD then import them on the new laptop?

2. Or will EXPORT on Callibre choose ALL of the Callibre books instead of just the new books? Will this result in duplicates being added to my library on the new PC?

3. What is the best way to keep two HDDs synced? One external HDD will go to a relative's house, and the second HDD will go into my fireproof safe. I do not trust "Cloud Storage". Do I use the same Export process to keep the HDDs synced? Or can I click and drag the libraries, because only a few books at a time will be added. I don't know how to keep duplicates out of the HDDs. How would I remember which books to add to the HDDs?

4. Is there a better way to move libraries and keep the HDDs synced? I have never used an external HDD with more than 1 computer.

TIA