Gokul43201 said:
They have the same grammatical structure but there's a difference in content. In the first and last sentences, the two clauses are both characteristics of "you". In the other sentences, the first clause refers to a characteristic and the second clause refers to an outcome of that characteristic.
I was just being a smart***, but sure, I would have looked for a rule at work on something I hadn't considered yet.
1) You speak eloquently and have seemingly read every book ever published.
2) You are a fountain of endless (sometimes useless) knowledge, and never fail to impress at a party.
3) What people love: You can answer almost any question people ask, and have thus been nicknamed Jeeves.
4) What people hate: You constantly correct their grammar and insult their paperbacks.
In (1) and (4),
and is the familar truth-functional one, so for one thing, you can switch around the phrases without changing the meaning, e.g.
1a) You [speak eloquently] and [have seemingly read every book ever published].
means the same as (is equivalent to)
1b) You [have seemingly read every book ever published] and [speak eloquently].
I agree that there's the additional info in (3) that the second phrase is a consequence of the first, so switching them around would require more changes, and that
and is not truth-functional. It's not as clear to me whether or not the same was intended in (2), but it could be that this person included the commas (consciously or not) to encode that cause-effect relation. Just my first thoughts anyway...
I had no answer to about half the questions, so it wouldn't tell me what I am.
Isn't that your wife's job anyway?

A Belated Congratulations too!