Thanks for supplying the context. You're correct in your understanding of "over his milk".
The oxcart question is not offensive in itself, though it is colloquial and hence sounds a bit silly.
The key sentence in the larger context you provide is "She had, for almost two years now, baited him. In the halls, in the elevator, even in his own office, into which she romped now and then like a circus horse, she was constantly shouting these silly questions at him."
To bait someone is to deliberately taunt or annoy them, hoping to get a response from them. (Analogous to offering bait to a fish in the hope that it would bite.) She behaves extravagantly ("like a circus horse"), she shouts out rhetorical questions that are both colloquial and hackneyed, and ultimately she is always asking the same question that assumes things are going badly. She's negative, imposing, and annoying.
At least that's my take on it, based on a few paragraphs. I have to admit that I've never read that classic story before.
Given that your source says that it was published in The New Yorker, I imagine the author is American.
In Europe, floors are described as follows: ground floor (street level), first floor (first floor above street level), second floor, third floor, etc.
However, in America, they call the street-level floor the first floor. So if the publication is American, then "first floor" will be the ground floor.
As for "down the hall" it means "along the hall" in this context. So it's further along the hall, not necessarily at the end. It could be at the end, but all it says is that it's closer to the end than the current position is.
Here's a diagram for example:
Doors 1-3 could be described as "down the hall" from a person standing at X. Door 5 is right next to him so it wouldn't be described as "down the hall". Door 4 probably wouldn't be described as down the hall since it's a bit too close, but it could be.
Best Answer
Answer
This question is from James Thurber's The Catbird Seat. The original text is as follows:
This clearly shows that he did not injure her in any way, but merely surprised her and shoved her. The following is from Critical Semiotics, Lecture Eight: A Semiotic Reading of James Thurber's "The Catbird Seat" by Scott Simpkins1
This is a tricky sentence to interpret because there are two meanings of "a football tackle: a verb and a noun." (AmEng). In addition, your reference to "swift move" and "football tackles on YouTube" got pretty much everyone2 thinking in terms of the verb. (A verb-ish meaning could make sense, even though it would be awkward. It would be similar to "a train wreck" which is a noun form of "The train did wreck." This is sometimes used like this, "The movie was painful to watch; it was like watching a train wreck in slow motion. You knew it was going to end badly.") Here are two definitions for "football tackle".
The proper interpretation is the noun form. The sense of the sentence is like, "John ran like a cheeta." Also note that a "rush" in football is a play in which several tackles will rush (run quickly) towards the quarterback to grab him and take him to the ground (tackle him).
The word "like" is important, since that suggest an simile, wherein one thing is similar, but not the exact same as, another thing. If one says, "My brother ran like a cheeta" we don't think he really ran as fast as a cheeta. We know that means he ran very fast. So "like" describes how he rushed: like a tackle might rush towards a quarter-back. He bumped her as he passed her. It's an aggressive and surprising movement for sure. However, it was certainly not as fast or aggressive as a football player. And importantly, he did not tackle her or even attempt to tackle her! That character had enough of being intimidated by her, and the bump was to show her that he wasn't going to put up with her domination anymore.
1. A "semiotic reading" would (roughly) be one that analyses what is meant, symbolically.
2. @snailplane determined correct interpretation. @J.R. helped bring to my attention with co-editing.
Additional "Advice"
I would like to offer some additional advice, since I've noticed that you're asking quite a few questions from famous short-stories that may be somewhat advanced for you. It's difficult to give you a good sense of what's going on without more context, and typically these books are studied in class situations where themes play an important role in understanding.
The details of what these "mean" both literally and figuratively have been covered by analyses that are available on the web, and you might want to start there first. Also, you may find famous stories such as this one (and commentaries about them) have been translated into (or written in) your native language as well.