It mostly comes down to pacing and how detailed you get with the story. Lord of the Rings can easily be chopped down into a single book. It's about the content and not just fluff content, but good relevant content to the story that keeps people interested. Let's take a look at your questions
When turning a single book into a series, what changes must be made to pacing and story structure?
The pacing, if you want a one story epic arc like LoTR, needs to be slower, significantly slower. That isn't to say you add in all the boring details, but you need to expand on the important events. Add in more skirmishes between armies, add in new, more key event plots. Spend more time explaining important elements. Add subplots and layered stories. If the MC has a background (Aragorn's background story), use that to help build the richness/depth of the character instead of lightly touching it as you may in a single book. Have it be a reoccurring and growing subplot that boils into the apex of the story.
Where should the split point(s) be?
This is something only you can address. Think of your story in acts. Where would be a good cliff hanger? Where would be a place that if your first book ended, I am running to the store to buy the second book? Reflect on LoTR again, the second book ended with Sam hiding as the orcs came and took Frodo's webbed and unconscious body away. Cliff hanger. What is going to happen to Frodo? Is it all over since he has the ring and was captured? We don't know.
How make single books satisfying?
What satisfies you when you read a book, in particular a series? Each book should be an act, a sub segment of the greater story. As I stated with one of your earlier questions, adding subplot helps to create great individual books. The subplots have all the elements of a story, but the main plot is still growing. The subplot climax is resolved and the heroes can continue on their journey into the next book as they climb the main plot.
As with any book, what makes a book satisfying is not letting your reader feel cheated by skipping/rushing events, but not going too slow over boring topics. Pacing and quality writing that is well organized leads to satisfied readers. If the topic is boring, if the material isn't good, no matter how well written it is, the readers will lose interest.
Does every book need to repeat the three act structure (presentation, conflict, resolution)?
Yes, to some degree. Possibly not a resolution, or a resolution to the main conflict, but it does need to follow the normal flow of a plot. As stated in the last question, some times ending on conflict draws readers into the next story followed by immediate resolution of the subplot and continuation of the cycle.
How to keep the reader interested?
As I have stated several times, interesting stories, and quality writing is how you keep a reader interested. Pacing of the story, action, cliff hangers, tension, release. Maybe not every story needs to have a ton of elements to it, but I have found the best stories utilizes all the emotions a person feels at the right times a person should be feeling them if they were in the story.
As with running a business (location, location, location) a story is all about content, content, content. Not just content but also, the delivery of content. I can go out there and tell a joke and no one laughs. You can say the same joke, to the same people, and get the whole room rolling on their backs. Bottom line is that story telling is like a good joke, if it is told well, people will be interested and satisfied.
Also some advice that really stuck to me from one of our own (Mark Baker), "Not everyone will enjoy a rhubarb and pickle cookie. A lot of people though want a really good chocolate chip cookie."