No, there is no restriction on belt colors in the US. In some styles, red indicates a level in the kyu range. In traditional Okinawan karate, red indicates someone that is 9th or 10th degree blackbelt.
Yes of course
Yes, there can be. In certain styles, (mine for example, Shorin-Ryu) red is typically used to signify 9th and 10th Degree, or 10th Dan. Technically, there should only be ONE 10th Dan in any style, and that is the founder, or the person who has taken over after the founder has died. In most of the Okinawan arts, there is a belt in between black and red. It is a white and red belt worn by 7th and 8th Dan karateka. Ninth Dan wears a red belt as well. We are fortunate to train with a 10th Dan from Okinawa that has been teaching in the US for over 35 years. The head of the style in Okinawa awarded it to him 9 years ago.
American Kenpo Karate.
Because it is on the US Endangered species list, yes.
"Rejected"
There are tens of thousands of karate students in the US alone.
Black belt is a term used in the martial arts of Korea and Japan. Kung Fu tends to award sashes rather than belts. And many schools do not run promotions as Karate does.
It is not illegal in the US.
The first recorded demonstration of karate was in 1932 in Hawaii, then a territory of the US. There are very likely to have been practitioners here before that.
it teaches us 2 be relaxed and ready
no it is not illegal
Karate is not one of the Olympic sports. Taekwondo is an Olympic sport and the US is participating.