I'm seeing from various translations that
est-ce que vous en avez assez
is "Have you had enough?"
whereas
est-ce que vous avez assez
is "Do you have enough?"
A couple questions:
Can I leave the pronoun off of the second sentence? As in "Do you have enough (of the previously mentioned thing)?" or should it always include a noun/pronoun.
Why is the first sentence "Have you had enough?" and not "Do you have enough of it?"
In comments @None noted important elements to answer this. My answer was meant to serve a different possibility from an answer that has since been removed. To save the information about this, @None wrote:
You can't leave out en in the second sentence because en is the pronoun that replaces whatever you are talking about. I expect this answers your n°1.
Your n°2 is not quite clear. Did you mean : "Why is the first sentence Est-ce que vous en avez assez? and not Est-ce que vous avez assez de cela?. If so the answer would be the same as answering why is it "Have you had enough?" and not "Do you have enough of it?" in English: Est-ce que vous en avez assez? is more usual (as is "Have you had enough?" in English) but you could encounter contexts where Est-ce que vous avez assez de cela? would be acceptable (as would "Do you have enough of it?" in English).
En replaces whatever you are talking about. Let's imagine I'm buying potatoes by weight. In English the sales person might ask "Do you have enough" ("potatoes" is implied but there's no need to mention it English), in French they'll ask est-ce que vous en avez assez ? because you just cannot omit it, it has to be mentioned, it's either est-ce que vous avez assez de pommes de terre ? or est-ce que vous en avez assez ?
Est-ce que tu en as assez ? En as-tu assez ? As-tu assez mangé ? Est-ce que tu as assez mangé ? Just as said in this answer I pointed to previously : "You can't use that sentence without either the pronoun en or what it replaces."
Can I leave the pronoun off of the second sentence? As in "Do you have enough (of the previously mentioned thing)?" or should it always include a noun/pronoun.
You might but that would be colloquial, oral French. What it is about is implicit and is almost always money, e.g.: C'est 15 euros. Est-ce que vous avez assez ?
Why is the first sentence "Have you had enough?" and not "Do you have enough of it?"
Because that's the most common meaning of this sentence, an idiom here. The regular meaning is also common: "Do you have enough of it?" Which one to pick depends on the context.
Context is key. You could see a lot of translations without more context.
For example, "Have you had enough?" could mean en avoir assez, a fixed idiomatic expression equivalent to have had enough figuratively, as in "to have it up to here" enough, or "enough is enough." Ras le bol has a similar meaning. In this meaning, you cannot leave out the pronoun.
From TLF :
B. (En) avoir assez de qqn, de qqc., de + inf. 44. Je crois que son mari en a assez de la cohabitation avec ta mère. MAURIAC, Le Mystère Frontenac, 1933, p. 178.
Imagine a dialogue:
—Je suis vraiment crevée. Je bosse sans arrêt, il y a trop de glandeurs au bureau et le patron s'en fiche.
—Ce n'est pas facile. Moi aussi j'en ai assez. Boulot métro dodo, à quoi ça sert ?
—Toi aussi, tu en as assez ? Il faut agir, j'en ai ras le bol de cette hypocrisie.
In en avoir assez, the en is fixed. The pronoun implies enough [of it all]. The phrase may be followed by more ("j'en ai assez de ces nouvelles !") but keeps the pronoun en. For general uses of en I also refer you to the already linked question.
Your translation of have you had enough vs. do you have enough could point to this sense.
