I just wanted to ask if Prince of Fools (The Red Queen’s War, #1) closely related to the Broken Empire series? In other words, should I start with The Broken Empire series before reading Prince of Fools?
Prince of Fools (& the Red Queen's war trilogy) do have links to the Broken Empire trilogy, including cross-over characters and different looks at the same events.
However, it's entirely possible to start with Prince of Fools and to save Prince of Thorns (&King &Emperor) for later or never.
It really depends if you feel Prince of Thorns will be too dark for you. The protagonist, Jorg Ancrath, would be the villain in most books. Prince of Fools has a cowardly womaniser as its 'hero' and offers more laughs between the covers.