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.
"Get the basics straight" and "Get the basics straight first" are valid English, but are not idioms. In a context where an author is trying to:
- Be polite (perhaps sarcastic, but neither rude nor obscene nor profane)
- Point out the basics of something, before pointing out more advanced features
- Write clearly
- Use the second-person imperative
"Get the basics straight" or "Get the basics straight first" is a natural thing to say.
Here are some alternatives that are idiomatic. Notice that some of these alternatives are quite rude, or compare the reader to a baby, toddler, or young child:
- You have to crawl before you can walk.
- You need to walk before you can run.
- Learn the ABCs of <topic>
- Get your shit straight.
Here is an idiomatic alternative that is polite:
Best Answer
Put my nose to the grindstone.
Knuckle down.
Put my head down.
Get stuck in.
Get in the zone.
Throw myself into the task.
Really go at it.
Put everything into the task.
Etc