Learn English – Pulling teeth vs Pulling nails

In poker, at the end of each hand, the winner "lays their cards out on the table" to show they've won. Since part of the game of poker is to try to disguise your hand from the other players, when the winning hand is laid on the table, this reveals facts that previously have been hidden or even deliberately lied about (through bluffing) by the players.

This leads to a common idiom, "lay your cards on the table" to mean showing your actual capabilities. In a negotiation, this idiom can mean revealing your actual wants and what you're willing to give in return.

The idiom is also used in a more general form, "lay [something] on the table" and with a broader meaning, to reveal things that are hidden or simply to speak plainly.

In your examples, there are people who might not normally reveal their true beliefs, and the writers are using the idiom of putting them "out on the table" to mean expressing those beliefs openly.

"On the Table" also means for something to be subject to discussion or consideration by a group. In the written example you provided, the characters views about premarital sex were "on the table". I would infer this is not a subject matter they speak often about.

Is “in one go” British English or just English?

I've wrestled with this one, mostly because of the way you've titled your question.

Take, for example, nappies (which we call diapers in the U.S.). I would consider nappies to be UK English; I rarely hear the word, and, more importantly, when I do, I almost have to translate it in my mind.

As for in one go, I looked at a lot of blogs and message boards, and, indeed, when I managed to find this expression on the internet, it was almost invariably traced to a U.K. speaker¹. But, for some reason, it doesn't sound chiefly British to me. It's immediately understandable. I got this done in one go doesn't sound like something I would never say, (unlike, I need to go change a nappy).

So, getting back to your title, I find myself wondering: What makes something "British English" vs. "just English"?

If I had to make a ruling, I'd say, no, "in one go" is not "British English", and I'll count on Macmillan to back me up.

Here is the definition of nappy in the American version of Macmillan:

Now here is the definition of the noun go in the same edition:

So, the Macmillan editors, at least, don't seem to think the phrase is British enough to be tagged BRITISH.

That absence of a BRITISH tag doesn't appear to be an oversight, either; that same entry also reveals:

In short, Macmillan would categorize

I'll have a go at answering this question

as British English, but

I typed this whole answer in just one go

would be what you called "just English."

Based on my usage searches, though, I think it's a borderline call, so I wouldn't vehemently argue against Codeswitcher's stance.

¹Like this one, from an electrician:

In the latter case, then you'd be doing yourself a favour to have the whole lot done in one go.

The speaker is a self-identified electrician from Thornbury, which I assume is a U.K. Thornbury, judging by the way favour is spelled.