Can we omit “at” and just say “…minutes before…”?

In the first example, absolutely… personally, I think it sounds better or more natural. But in the second one, it sounds more natural to keep the “at” in the sentence. Honestly, it’s pretty case-by-case.

Most of the time, yes, and you'll be understood just fine. The scenarios where I think it's preferable to include the "at" is when you're talking about a specific time or a sequence. To further the first post "At two minutes before the curtain goes up, 'places' is called. At 1 minute, everyone is on their mark and silent. At 30 seconds, the music starts." "Before the curtain goes up" is implied in the second and third sentences. "Two minutes before the curtain goes up, 'places' is called" is fine on its own when not part of a larger sequence. "The airplanes came 5 minutes before 6 yesterday morning" is fine. But "The airplanes came 5:55 yesterday morning" really needs an "at". It would be understood but is clunky.

Omitting "at" in the first sentence would also sound fine, but using "at" in this way is evocative of reading a schedule. We would often say "at 1:00 PM we ate lunch, at 2 PM we went to the beach", etc., and using it surrounding an event is similar; "you're all expected to be at your places at five minutes before the show starts". In the second sentence it would sound weird to me to omit the "at" but everyone would still understand the meaning

I'm unsure if there are grammar rules here if you're answering a test question, but if you're just saying these in conversation, the "at" seems optional. They sound good with the AT and without the AT to me. Neither seem weird.

I'm not a linguist, but as a native speaker I would not say "at" and would just say "minutes before". It doesn't sound wrong to me.

Both sentences would make sense without the "at," and most people would probably omit it, but they do both make sense as-is. In both instances, "at" is being used because the events are happening at a specific time on the clock. The first sentence is probably not a super familiar phrasing to most people, because it is very theatre-specific. In the theatre industry, we use phrases like "two minutes to curtain," "ten minutes to curtain," etc. in the same grammatical way that a specific time like "5:00 PM" would be used. So saying "At **5:00 PM**, 'places' is called" would be structured the same way as "At **two minutes to curtain**, 'places' is called." Saying "At two minutes before the curtain goes up..." would be superfluous in a theatre setting, but still technically makes sense. In the second sentence, "5 minutes before 6" means "5:55," so the same structure of using "at" to refer to a specific time is used.

On the second one, you could omit the at, but in my opinion it slightly changes the meaning. "At 5 minutes before six" simply tells you the time it arrived, 5:55 "5 minutes before 6" kind of implies that 6 is the default. You might use it if the schedule says 6, but the train actually got there 5 minutes early. It's subtle, and not everyone would necessarily interpret it as I do. In speech, you will be understandable with or without the "at."

In English, you can say [at (time)] to indicate an action happening at a certain time. You can also indicate a certain time by saying [x minutes before y] and so, even if saying [at x before] is grammatically wrong, it is not wrong to say [at (x before y)]. The rules apply inside the bracket, then consider the bracket as a single grammatically correct unit of time to which (at) can be added.

For the first example, using "at" in that way is a convention in the theater industry. It would be correct without it, but it's also correct and common with it.

"At two minutes before curtain" is stage jargon; "at" indicates that you're referring to a specific point on the stage manager's countdown. Without it, it just means it happens roughly two minutes before the curtain goes up. Which is fine, honestly. You can omit it without any trouble because the meaning is close enough. In the second example, the planes came at a specific time. That time was five minutes before 6am. Without 'at,' the planes came five minutes before the clock struck six. Here again, it ends up meaning the same thing so it's fine to omit it.

i wouldn’t say it that way, but maybe it’s theater and pilot jargon usage?

Those are two slightly different uses. In the first example, it is referring to the location of a point in time in relation to another movable point in time, and the “at” can be omitted. The second example, while it looks the same, is actually naming a specific time. You could substitute 5:55 and it’s exactly the same thing. You need the “at” when referring to a specific fixed time. You wouldn’t say, “the train arrived 4pm”, or “the sun sets quarter past 7”. If the second example was explaining the time in relation to another movable time, you could remove the “at”. For example, “the train was scheduled to arrive at 7:15 but arrived 10 minutes before that.”

Yes.

I may be wrong, but in this case I believe they use 'at' to indicate it is a static event that happens precisely 2 mins before. Saying just "Two minutes before..." could mean it's less precise. It's tricky, here it just means 'places' is a particular event

The "at" indicates timekeeping. It is non-optional in a phrase like "at nine o'clock she got dressed". So \*with\* the "at", "five minutes before six" is a clock indication. \*Without\* the "at", "five minutes before six" is a modification on a clock time. By analogy, you could say you're at The Golden Gate Bridge, but you couldn't say you're at five miles from the Golden Gate Bridge, unless Five Miles From the Golden Gate Bridge is its own landmark. So when you say "at five minutes before six", you're referring to "five minutes before six" as its own "landmark", in a sense.

Sure! For the second, I’d probably replace at with in just to make it flow, but overall removing at seems more natural

Using "at" signifies that reference is made to a specific clock time. Without "at" the reference would be to a period of time.