In-the-money runs in the opposite direction from a call, and stating it the wrong way inverts the whole page. The SEC's rule for puts is the mirror image of the rule for calls: a put option is in-the-money "if the strike price is above the actual stock price," and out-of-the-money "if the strike price is below the actual stock price." At-the-money again describes the strike and the current price sitting at the same level. A put's intrinsic value, like a call's, is zero unless the option is in-the-money.
A put buyer's maximum loss is capped exactly the way a call buyer's is, because the mechanism is the same: a right, not an obligation. The buyer pays the premium once and can lose no more than that if the right expires unused. What differs is the direction of the bet: a put pays off as the underlying falls, so buying one is generally either a wager that the price will drop, or a way to protect an existing holding against a drop, a use commonly called a protective put. Buying a put on shares already owned works like an insurance policy: it costs the premium, and it puts a floor under how much the position can lose, because the holder can always sell at the strike regardless of how far the market price has fallen.
A put writer's loss is large but bounded, and the bound is set by the fact that a stock cannot fall below zero. A writer who sells a put receives the premium as the most they can make, and if assigned, must buy the underlying at the strike even if the market price has fallen far below it. The worst case is the stock going to zero, in which case the writer has paid the full strike price for something worth nothing, a large loss but one with a defined floor, unlike an uncovered call writer's exposure to a stock's unlimited upside. Selling a put is therefore sometimes used deliberately by an investor who is willing to buy the underlying at the strike price anyway, treating the premium received as compensation for making that commitment.
Breakeven runs the opposite direction from a call as well, and it is worth printing as a number for the same reason. For a put buyer, breakeven is the strike price minus the per-share premium paid, and the position is profitable only below that level, not merely below the strike. As with a call, the premium quoted on an options screen is a per-share figure, while the dollar amount actually paid for a contract is that premium multiplied by the contract's size, ordinarily 100 shares for a listed equity option.