Yes. This is correct.

To answer you bullet for bullet

1. Yes. This is what these do.

2. Yes, this is a correct reading, if you go from 18 to 20, you can still increase to 22.

3. Yes*, most things in 5e stack, though sometimes things don't stack with themselves (this isn't a bonus though, it's an increase, it's different). However, this is probably rare enough that this should not be an issue in a campaign (an if a DM gives out more than one of these per PC it's their own fault if their game breaks because of it). *I don't have this item's text in front of me so this is barring a caveat in the description, which if it existed would likely preclude this particular bullet anyways.

So basically, yes. This is an item (among several and a L20 class feature or two) that breaks the normal rule for maximum 20 ability scores. It breaks it, and it does so permanently for the character.

RAW allow it, but there are some setbacks.

Crawford also agrees (thanks to V2Blast for that).

Grier: If you find multiple books or are long lived, can you get this bonus multiple times?

Crawford: Yes.

While you have done an excellent work in tracing the requires rules and components to make all of this work, there are somethings you need to rethink.

3200 years is an immensely long time.

Consider that, every time the Wizard freezes himself in time in his dimension, the entire world ages a century. Civilizations rise and fall, continents change, plagues ravish, dragons destroy. Industrial revolutions rise, ice caps melt, Gods wage war upon each other. While your Wizard could ignore all of these, someone that didn't take a long time every century to follow up on all of these events would soon find themselves completely lost in the world, not knowing where to turn to anymore, and only imagining how the carriages without horses worked.

Learning all the books takes a long time every time, where food, water, safety, and above all sleep, are necessary.

The Wizard cannot just spend 300h studying books. By the 5th day, he'd die of exhaustion (seriously, by RAW, 5 levels of Exhaustion kills you!). He needs to rest everyday, to take care of his health, and would take a lot more time than the minimum you've allotted.

After a few centuries, the Wizard can barely describe a place to appear at.

Imagine he had a home to come back to. After a century, it's probably been taken over by some other resident. After another, maybe it's been abandoned. Another and it is now the home for devils and mindflayers. The nearest town has grown to a big empire. In another century, it has waged war and dwindled in size. In another, a plague has consumed anyone who was left there. As the world changes, the places the Wizard has to come back to all vanish. He can always come back with some general description, but he has no real place to come back, no place he can recognize. He stops knowing how the world behaves, he doesn't know what is dangerous anymore, and how to fight the new threats.

Does a sane man really want to throw everything away to become powerful?

Every story has a big villain. Some demon risen from Hell (Tarrasque), some alien from another planet (Megatron), some angel fallen from grace (Sauron). Your Wizard would become this villain. He attained immense power over the centuries but lost touch with the world. All he has is power and the strength to use it, but he isn't part of this world anymore. The new races who have emerged will barely recognize him. He cannot bond with anyone, as everyone is so dumb and boring compared to himself. He is, in all respects, a higher being. What does he want to do now? Control the world, for the greater good? Or destroy it?

How would the world see him?

A creature emerges out of thin air. Taller, stronger, grander than anything these primeval races have ever witnessed. The air around him fizzles with raw arcane powers. He speaks a forgotten language, no one comprehends it anymore. The crowd gathers in awe. A flash of flames appears, an exhibition of his skills, but most of the crowd looks scared, and starts moving away. This alien god looks angry at the lack of adoration by these puny creatures. In a swift gesture, all of them are incinerated. They will bow down to their new leader or perish. Accept this wicked salvation or be destroyed.

This is how villains are born.