A Wizard has a spellbook and an education.
A Wizard has a spellbook, he does not need to have an education. The rules also state the form and function of the spellbook are not fixed:
"It might be a plain, functional leather volume that you received as a gift from your master, a finely bound gilt-edged tome you found in an ancient library, or even a loose collection of notes scrounged together"
I have also had spellbooks be made of stone tablets and collections of bones.
Those are elements that specifically affect story. (Edit: Hence my "Dwarf Sailor Wizard" example above. Dwarves are generally not strongly associated with academic education, but rather with excessive deference to ancient tradition, and Sailors are generally not known for being well-educated, instead needing a strong back and, ideally, the ability to sing well.)
There is no need for education. The word "education" is not mentioned at all in the Wizard entry on the PHB.
That said, the idea of a sailor or a Dwarf being not strongly associated with education (or Wizardry) is a stereotype. It is fine to lean into that stereotype, but it is also fine not to and to deviate from it.
Not at all. The "Oath of Devotion"--devotion to what? It can be almost anything.
It is listed in the subclass description. Oath of Devotion is actually one of the most restrictive Paladin oaths:
"The Oath of Devotion binds a paladin to the loftiest ideals of justice, virtue, and order. Sometimes called cavaliers, white knights, or holy warriors, these paladins meet the ideal of the knight in shining armor, acting with honor in pursuit of justice and the greater good. They hold themselves to the highest standards of conduct, and some, for better or worse, hold the rest of the world to the same standards. Many who swear this oath are devoted to gods of law and good and use their gods’ tenets as the measure of their devotion. They hold angels — the perfect servants of good — as their ideals, and incorporate images of angelic wings into their helmets or coats of arms.
Tenets of Devotion
Though the exact words and strictures of the Oath of Devotion vary, paladins of this oath share these tenets.
Honesty. Don't lie or cheat. Let your word be your promise.
Courage. Never fear to act, though caution is wise.
Compassion. Aid others, protect the weak, and punish those who threaten them. Show mercy to your foes, but temper it with wisdom.
Honor. Treat others with fairness, and let your honorable deeds be an example to them. Do as much good as possible while causing the least amount of harm.
Duty. Be responsible for your actions and their consequences, protect those entrusted to your care, and obey those who have just authority over you."
So RAW if you are playing Oath of Devotion, once you reach 3rd level the oath above
"binds you as a Paladin forever"
The class also has consequences for breaking the oath to include potentially
"being forced to abandon the class". This is the only class I know of that has words to this effect in the description.
If you are playing levels 1 and 2 before your oath you are right, the oath is irrelevant, but the PHB addresses this to by saying some Paladins do not believe Paladins to be true Paladins until they take the oath.
And it's explicit that you can come up with your own oath, as long as it's consistent with the overall concept presented. It doesn't have to be word for word the same.
I don't see that in the PHB, but it is possible I missed it. Do you have a reference for this? I would think this would clash with the subclass as the oaths listed in the PHB are presented as integral parts of those subclasses, not as concepts.
But that's my point. You make it sound like the Wizard uniquely has no limits at all, which is false and that Paladin and Warlock are insanely hyper-limited,
Not the Wizard uniquely - Wizard, Bard, Monk, Rogue, Barbarian, Fighter, Sorcerer, Druid and Ranger have pretty close to no story limits. Cleric has a few (mainly the requirement for a Deity) but it is closer to none than it is to Warlock or Paladin which are the two classes that are hyper-limited RAW.
. They're all on a spectrum, nothing is at either extreme (no limits at all; no freedom at all), and they're all much closer together than you claim. That's why I'm so confused here.
Nothing has no limits at all, but everything except Warlock or Paladin has very few story limits IME.