Yes, but it has to be model specific (specifically what the model looks like)
Yes, and they could be anything from best quote said by the character, songs sung by or including the character,trivia (the different character's movie theme ), or of course Special themes which would include the model/their picture and depending on
Yes, but they should not be model based challenges (for example trivia (various), popularity/polls, who can get the highest score in various games/ puzzles)
No, just stick to whatever the regular game play is.
other (please comment your ideas :) )