Uhoh. Behind already!
Good thing these questions can be answered with the same book.
Favorite Monarch: Emperor Gregor of Barrayar. His deadpan melancholy makes him one of the most human of fictional monarchs and he is the perfect foil for Miles's hyperactive genius. And damned if he doesn't steal every scene he is in.
Best dinner party also in this book. If 'cringing with second hand embarrassment' can be considered the same as best. I tried to think of something more sophisticated, like Babette's Feast or something, but no, I got nothing. Miles it is.