Princesses do collect taxes, but it's like being a landlord. You can be a shitty landlord and never repair the plumbing, just collect the debts. Or you can be interested in your tenants not rebelling and smashing up the place. Of course, it's a balance. If you let people walk all over you suddenly you're the one spending and the kingdom runs out of money, or you can on the other extreme run out of other people's money from overtaxing and being cruel.
One of the most important roles of a medieval princess was the dispensation of charity which was considered her participation in social life.
So, basically, they did their research. King usually manages the stuff like building roads and the military. And the queen... gives male heirs. Except sometimes when she's had enough, and rules instead of the king. Happened a few times. Speaking of queens who ruled, there was a whole movie about Christina of Sweden. She was really hardcore, and eventually wound up abdicating after they forced her to choose between a guy she liked and an arranged marriage. Also, she was kinda bisexual.
Oh, and garum that is with plums is fermented fish sauce (probably similar to the stuff in Thailand, Vietnam, and Korea). That he addressed the king about it (and not the cook) is probably code for "I need to talk to you privately." In fact, given what happened after, I'd say so.
I think there's only two endings so far, but there should be five or so. You can do everything but piss off your mom and get the perfect ending.