Regarding the leg injury, I think we read that she stumbled and fell a fair bit while she was blindly running around. I wouldn't be surprised if she has scraped her knee and/or grazed her shins at least. On getting stuff from her place - it's already established that several of the servants were loyal to Violette rather than the Duke, so the same network that let Marin know to come to Violette at the hotel would be getting her things to her. I can't see the duke objecting to the servants packing up and clearing out Violette's stuff, especially if they let him assume it's all going into storage. And finally, Yulan's finances - if I remember correctly, he is officially the son and heir of a wealthy aristocrat as well as the illegitimate son of the king. Even if all he has is an allowance, he can still tell the hotel to send the bill to his adopted family and it'll get paid. I admit I don't get the title either.