1.) The Dragon Flagon specifically says in the rules that it's dropped when the character holding it is knocked down, dazed, etc. Does this rule apply to mugs and chairs as well or are they always in the possession of the character who picked them up until thrown?
2.) In a 2-player game, is the score tallied as a total of both players' characters' reputation as outlined in the team game?
1) Nope. The DF is special, and magically goes back to the center space. (page 9)
2) "Each player adds the total Reputation for all the characters they control." (page 9)