Baggage: Given that I am allowed to bring one personal item and one carry-on item on the plane, am I allowed use my laptop bag for books and put the laptop in my backpack?

It completely depends on the airline.  The "personal item" concept is very much an American concept - in much of the world, you gat one item only, with no distinction of what kind of item. If there is a "personal item" allowance, the airline won't be going through the carry-ons to see if they match the concept.  But they will look on the size of the bags....two big bags does not fit the concept of "personal item".

Oh yes: my wife and I like taking random interesting trips, and often fly Spirit. They're almost as bad as Europe's Ryanair, but they're cheap... anyway, Spirit is one of those "one personal item..." airlines. I've absolutely stuffed my laptop bag with clothes and a Kindle and toiletries, and it's always worked... I can fit a whole weekend's worth of stuff in a laptop bag, no problem...

I have travelled extensively and never been questioned as to the contents of the carry on items. I have often used my atop bag for other items and not a laptop. As long as the bag meets the requirements for the airline, i.e. weight and size, they have been accepted.

One guideline I have often heard is that one of the items must be small enough to fit under the seat in front of you, while the other goes in the overhead.  That is their main consideration, in my experience.