1. It's still called NAS team, but since the NAS team involves people from GKR across the state, then people may see it either NAS team or state team. Either one as long as you get the idea
2. This is quite long to type, but what I'm going to type I summarised from the Martial magazine, July 2003.
I read once that there is only one martial art ever existed in the whole world, the rest is the styles that people believe in (ie. like in religion). From the magazine, martial art itself can be studied under budo or bujutsu.
Bujutsu refers to martial arts studied for combat utility. Tradtionally, bujutsu is the art of war, and the primary goal is combat and to death. Bujutsu is the origin of evolution of modern martial arts. From what I interpret, it means trainings that goals are purely self-defence, such as the hybrid of many traditional martial arts to adapt to real situation (ie. real violent attacks), or ninjutsu training.
Budo has deeper meaning than just being able to do self-defence, I read the interpretation from many masters, they said it in different way, but if I sum up, the idea is same. Logically, the idea of budo is that you can't understand the word just by reading one material because you won't find the answer. The word is an abstract philosophy that you can understand by looking deeper and deeper.
The understanding of the word 'budo' is exactly the same as it is put in practice. One master, William J. Dometrich from Chito-Ryu said,' budo is a martial art that is studied for self-improvement through self-discipline required to master it over years of dedication, hard-work and study. Budo may also utilized as a form of self-defence, but this should not be the primary reason for studying budo.' There are many other budo interpretations by the karatekas in the mag.
Now about sparring. In the mag, there is an interview with the recently passed-away Sensei Keinosuke Enoeda from Shotokan. According to him, sparring is a sport that has very little relations if not none to self-defence. Sparring is more a test of abilities, abilities of mind and power control. He said sport karate is a definite aspect of karate-do.
Well from what I read in the mag and your question, I'm more curious now on how you define sport. For me, since in GKR we have sparring and we have tournament, and we follow rules which don't allow us for direct physical contact etc make the sparring is more like a sport (it also applies in olympic games). Sport for me is not about competition between people which end up some feel dominating the others. There's certainly win or lose in a competition, but by sport, we don't focus our winning just on how many medals we got, but it's more how we performed during the competition. Because in the tournament our goal is not to put down people, and we're assessed on our attitude as well. That's why there's such a word 'sportsmanship'. In the situation where I realise my odd of winning is not really high, instead of thinking 'I can't lose to this guy', I prefer putting this way 'I may win/lose to this guy, but even if I lose I won't give it easily'. That way if I do lose, I won't be very disappointed, as long as I have give all I have
To sum up, (this is purely my own personal opinion) GKR is indeed a budo martial art and it is not entirely sport, instead it has sport aspects in it.
I apologise if I make the readers bored or fall asleep

There might be some words that I put them ambiguously, coz it's near my bed time.
I suggest if you're interested in this, try to find the magazine, it's full of deeper meaning of martial arts than just being a fighting lesson.