Learn English – this side of something – meaning

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.

"Keep up the good work" is a nice expression, but because it's phrased as an imperative, it's one that can have unintended nuance.

One common use of this phrase is of a superior complimenting and encouraging an inferior in the workplace. For example, suppose your boss asks you to do a project, and you show her some preliminary results. She might respond:

This is what I'm looking for. Keep up the good work!

to indicate approval, but also to tell you that the project is not complete and that you should keep working on it. It comes across as kind of an order.

I agree that if someone is doing a favor for you, it can be an odd expression. It may sound like you're asserting authority over them, when they would rather feel like your relationship is as equals (or even that you owe them).

The exception is when someone is working on something that does not relate to your own benefit. For example, suppose a friend is doing a good job on a report for school. You might say:

Looks like you're almost done. Keep up the good work!

as a way to encourage her to complete the report. In this case it's more like similar expressions such as "Don't give up!" or "Hang in there!", which, while phrased as imperatives, are not interpreted as orders.