Solo Dodo

FWIW, only grand prince I An's character description page (linked from the Cast page) on MDL has an alive-or-dead Status (under Biography in the sidebar). None of the other character descriptions have this feature.
https://mydramalist.com/character/grand-prince-yi-an

I'm intrigued by your speculation, but find the death of the former king to be the most problematic. We saw the Queen Dowager light the fire. When she left, the king was still alive and presumably able to save himself. So there would have to be a Min assassin already hiding nearby to take out the king, and escape unnoticed. This is possible, but quite a stretch indeed!

Foul play exists

I think the 2ML usually loses to the 1ML in chess on purpose, but this time he went all-out as a subtle message to his friend that they are now rivals. Of course, he doesn't have a chance to with the FL's heart. But he will do much damage before he realizes his ambitions are doomed to fail.

Methinks the Queen Dowager doth protest too much! She has had the hots for Grand Prince Yi An since before she married the former king (who she found entirely unattractive). The frisson irks her as much as it sends a thrill up her leg because she wants him but must maintain her composure—she cannot have him! She want's to keep him close, and hopes a calculated arrange marriage will neuter him—but the last thing she wants is having to watch the grand prince happily in a love match with a woman outside of her control!
https://mydramalist.com/character/yun-i-rang

Read their character descriptions (backstories), linked from the Cast page. Her's provides a lot of insight into her motives and feelings for the ML which may answer some of your questions:

https://mydramalist.com/character/yun-i-rang
https://mydramalist.com/character/grand-prince-yi-an

Tell that to the ML (grand prince)! His mother died when a truck collided into their car. The ML watched his mother die, begging to be saved. 😢

(There was an article with a description of the incident displayed in one of the episodes. Someone took a screen grab, translated it from Korean, and posted it here within the last day or two.)

I think she wants him married to someone she can control, not to someone who makes him happy!

Evil? Try frustrated! She married a dude she wasn't attracted to (apart from his title, king) while being overcome with frisson whenever his brother (the ML) was near. Check out her character description (linked from the Cast page):
https://mydramalist.com/character/yun-i-rang

Plus, the guilt over killing her husband may be eating away at her soul. 🤔

OK, I guess maybe you are correct and she really is another evil queen mother… unless the former king is actually alive and faked his own death just to get away from her!

You can find it by clicking the Cast tab, at the top of this page, then click on Yi An's character name (underneath the Actor's name) to access the character description. All of the main cast & many of the supporting cast have linked character descriptions. Only Grand Prince Yi An has the Status button.

(I am viewing this on MDL.com via a web browser, and am not using the app.)

In this universe the prime minister is not elected democratically, but is appointed by the king from one of the noble families. Min Jeong-u (the 2ML) was preceded by his father and grandfather in this position.
https://mydramalist.com/character/min-jeong-u

This drama has the same amount of time to resolve all the plot layers as does a typical 16-ep series. There are fewer act breaks, but each of the 12 episodes are longer in duration.

The character description for Grand Prince Yi An implies that he may indeed die. Notice in the Biographical Information in the sidebar, you must 'Tap to reveal' his Status to see whether he is alive or dead!
https://mydramalist.com/character/grand-prince-yi-an

Of all of the character descriptions, his is the only biography with this feature. 🤔

"Although she occasionally wonders what life would be like if Yi An had been the crown prince instead, I Rang forces herself to suppress those thoughts and remain loyal to the future she was raised for. Yet as political tensions grow and Yi An’s position in the royal court changes, the delicate balance between duty, ambition, and unspoken feelings begins to threaten the carefully controlled life she has built."
https://mydramalist.com/character/yun-i-rang

I don't know about any of that. All I know is that I can't look away from her whenever she is onscreen.

* Grand Prince
https://mydramalist.com/character/grand-prince-yi-an

I agree. My big complaint in HdL was that her acting was eclipsed by her wardrobe. And now it's the other way around—IMO, her acting has greatly improved. (I did however very much enjoy seeing her strut in that yellow nipple shirt. Rawr!)

Maybe they know how assassins work?

I agree the pacing might be improved if we got 16 slightly-shorter episodes instead of 12 long ones.

Bugatti doesn't care about product placement. Showing some nefarious villain somehow hacked the brake pedal into a second gas pedal won't diminish their sales in the slightest.