The purple hearts represent her obedience.
She needs a certain level of obedience before you can get the 4th heart, and it's not so much being "mean" to her as it is options where you're treating her more like a dog than a princess that raises it, hence why some of the options which affect it are things like calling her a "good girl" or giving her commands.
"Why reinvent the wheel?" The entire heart system, their colors, and their meanings haven't changed since the Flash version, only the balance has been tweaked due to differences in the engines.
In the game, most of the princess's reactions (and dialogue bubbles with hearts) depend on her "mood," which is determined by three factors.
The first factor is the total number of hearts, from 1 empty to 5 filled.
The second factor is the color of the hearts, from red to blue-violet. This indicates "submission" (let's not forget the BDSM collar). This trait ranges from Selfishness to Servility. This stat ranges from 0 to 1, and can be thought of as a percentage. From the 4th heart onward, Pure Selfishness is no longer possible; "obedience" never drops below 30%.
The third factor is current arousal, not to be confused with the orgasm meter. It's also a stat from 0 to 1, and each appearance of a dialogue bubble with a heart (and negative ones even more) deducts approximately 10% of this stat. In appearance, this parameter can be seen by the red tint of the "blush" on the princess's face.
Now about interactions and dialogues.
Initially, what the princess allows to be done to her and the general reactions to dialogues depend primarily on the number of hearts. Without four hearts, it's impossible to completely undress the princess; after four, it's possible even on the first day. The more hearts, the more vulgar the requests.
Further, a shade of the heart comes into play in the reaction to actions and dialogues.
Most dialogues are divided into several types, 4 on average, with variations: Spoil, Praise, Scold, and Game Mechanics. Now, in more detail:
Spoil (dialogue bubble with a green heart, plus selfishness, or rather minus obedience, does not respond to arousal)
Praise (dialogue bubble with a blush, a change in the heart color towards 50%, can be considered normal, and increases arousal)
Scold (dialogue bubbles vary depending on the number of hearts and the shades, from shards to black hearts. Black hearts increase arousal the most; before 4 hearts, there are none, the heart color tends toward 100% submission)
Game Mechanics (undress, use tongue, display orgasm meter, change position, increase vigor, decrease ejaculation meter)
At the first heart level, you can only spoil and praise, otherwise the heart won't fill. And for requests to undress, even if refused, the heart's color will shift even to 100% obedience, but the number of dialogues themselves won't be enough. Punishments will almost be skull-destroying. A complete loss of arousal and, as a result, the absence of heart clouds that fill the heart.
At the second heart level, you can do a little more than at the first, but for the most part, it's the same.
Only at the third heart level can and should you actively turn the heart "blue"; the fourth heart won't open before 50% obedience.
Now about the "pain" parameter that the skulls cause. 5 hearts is a boost to arousal. 4 hearts is a minor boost to arousal. 3 hearts is a minor loss of arousal. 2 and 1 heart are a massive loss of arousal. To reset the pain/fear, you need to stroke the head; even 2 seconds is a complete reset.
Princess Pain is when you lift her legs too fast/too far, spread her legs or arms in the same way, and of course, spanking from behind. Parameter from 0 to 1, and 100% completely inverts everything positive and doubles the negative. In other words, with 10% pain, there is approximately a 10% chance that instead of a dialogue bubble with a heart, there will be a skull.
Just stroke the princess's head more often, this will also slightly increase her excitement.
Now, as for the "secrets," if you spend all possible dialogue options on clothes on the first day and bring the princess to orgasm once, there's a significant chance she'll "touch herself" in the bedroom on the second day. But if you use swearing to get to the first heart, nothing like that will happen. Although the heart will be blue enough for that to happen.