Scoring - hmm - well if you played a Tara you probably scored a LOT of times...no, that's not what you're asking.
Jim Carter assures there's no favoritism. The score sheets get input into a spreadsheet and automatically tabulated.
Advancing and/or winning Nascrag is a two part thing.
1 Roleplaying
2 Puzzle Solving and objectives
Roleplaying: Your characters have interactions with the other characters, they are listed on the character sheets. One of the Taras was jilted by Kiroc, she is hurt. Her sister is infuriated. Lootan Worships the ground Kiroc walks on. Kiroc treats Lootan as a lackey. Celledrus looks down on everybody a bit. Etc.
There are also things that happen in the event that should elicit a response from a character. Kiroc is charged with paternity. Lootan "finds himself" and actually ends up as arguably the most powerful member of the party, Celledrus discovers his wife is alive, his daughter isn't his, but still loves him and is missing. The Taras are killed by their mother and then later kill her (it's complicated). Roleplaying means those incidents should elicit a response. get in character and grieve, or celebrate, or whatever.
Stay in character as much as you can. The Toby winners for each character probably stayed in character at all times. Never say "my character says" etc. inhabit the role.
Puzzle solving and objectives: You are on a very short clock with puzzles. We don't want the action to bog down. If you get a puzzle, drop the roleplaying and focus. At some point you'll get a clue. Do you think a puzzle solved with a clue is worth as much as one solved without?
While there isn't a bonus for completing a round, there are points all through the adventure and if you don't get to them you can't score.
Why don;'t we share the score sheets? Are you kidding? Two reasons. We want people to just play. Not meta-game the scoresheet. We also don't want to be second guessed for every item on it. We all review the score sheets at the judges meeting and make modifications. It's the best we can do. It's a very subjective thing, a roleplaying tournament.