"how good is she likely to be?"
If she's very serious and spends hours training every day, it's possible she'll be close to Olympic level, but more likely, she'll be about the athletic level of a high school or college athlete. A good school will not allow someone to test for black belt until they're considered "mature", which can be anything from 13 to 18 years old, but it's possible she'll be a first or second degree black belt.
"What values are involved?"
Varies a bit, but hard work ("discipline") and honest behavior ("honor") are generally associated with "traditional" martial arts training. Think the willingness to make personal sacrifices of an Olympic athlete with the superhero-like "do the right thing" morality.
"Is there some sort of daily exercise you do every day? What is it?"
Modern karate training consists of the "three K's"- kihon, which are basic technique repetitions, kata, which are pre-arranged dance-like fight sequences, and kumite, or sparring, which is pretty hard to do without a partner. Okinawan karate systems (Goju-Ryu and Uechi-Ryu in particular) have a set of exercises called Hojo Undo, done with unusual objects, like gripping jars filled with sand to strengthen the grip. Outside of that, any sort of physical conditioning would be acceptable, like distance running, weight lifting, yoga, boot-camp-style exercises (common in karate classes), and even boxing-like training, like skipping rope and hitting the bag.
A note on kata: each different karate style will have a different set of kata. Look up the different styles on Wikipedia and cross-reference the kata on Youtube.
http://en.wikipedia.org/wiki/Karate_kata
On a daily basis, she might work out a bit in the morning by doing some running, exercises (with or without weights), then practice several repetitions of kicks, punches, blocks, and combinations, and maybe finish by hitting the bag or doing a kata or two, probably multiple times. In the evening, she'd probably train with a group.
"What's the mindset supposed to be?"
Depends. Some folks like to think they're old-school warriors and that every strike they throw should be intended to kill, and as such, they avoid any form of violence (including a lot of sparring) at all costs. Some folks treat karate as a physical art form, focusing on "perfecting form"- these folks would put a higher premium on athletic training. Some folks see it as a sport, and train relentlessly in sparring and/or kata. Some view it as a discipline, something just to get better at for the sake of being good at it. Most people feel all of these to varying degrees.
"What's the attitude towards emotion?"
Generally that it should be controlled.
"How is she likely to use her skills in a fistfight against someone with entirely different training? Someone with similar training?"
Whether they're trained or not doesn't change much, though a trained opponent is generally more dangerous. How she responds will depend on how she trains. If her school does a lot of scenario training- that is, "he punches/grabs your collar/chokes you and this is how you respond"- she may have build-in responses to those situations, but that's not really a "fist fight". How she responds there will depend on how her sparring sessions are conducted. A common form of sparring is light-contact point sparring, which will make her fast, but she won't be used to taking a punch, and maybe will have developed a bad habit of "pulling" her strikes, because you can actually get disqualified for hitting too hard under some rules. On the other side, you have "knockdown" sparring, which is full-contact: you can kick the legs, body, and head, and punch the body, bare-knuckle, but not the head. Some schools have incorporated kickboxing sparring into their training, so that might be something to consider.
American point sparring (if you fought this way against anyone who was trying to knock you out, you'd get knocked out):
http://www.youtube.com/watch?v=JlZWLHU-Qtg
Japanese point sparring (slightly better):
http://www.youtube.com/watch?v=9VsTLpVCfCo
Knockdown sparring (used mostly by the Kyokushin, Enshin, and Ashihara styles of karate):
http://www.youtube.com/watch?v=OsUOTV86K6Y
If her opponent is trained, what they're trained IN will be a tremendous difference in how the fight is likely to go. If they're a grappler/wrestler, they'll probably take her down and punch her out, or apply a choke or lock. If they're a striker, both fighters will try to keep it standing and hit one another.