Sorry UPRC you probably figured this out already but there are different colored keys for those specific doors, you can find them in dungeons or purchase them for about 1k gold a pop or (minor spoilers)
And yeah I love this game, I'm actually at the last dungeon but I've missed a ton of stuff so I'm combing through all the areas trying to find all the little secrets. Also in case anyone was curious the 3 classes you choose from do affect your stats:
Hero: 5 health / 3 magic
Prince: 4 health / 4 magic
Scholar: 3 health / 5 magic
And males get +1 to weapon power while females have -1 cost to magic. So there's a little variety, I think I've found at least one place where the gender of the player does matter, but I haven't been able to see if it's just a change in dialogue or what. ALSO you can change your hero everytime you load up the game, but the name you pick stays.