Until 1943 the Chinese Exclusion Act was in effect, prohibiting immigration of people from China since the time it was put in effect in 1882. Even though it was repealed in 1943, it wasn't until the Immigration and Nationality Act of 1965 that immigration of Chinese to America saw any significant increase. From 1943 to 1965 the Magnuson Act, which was the act that brought an end to the Chinese Exclusion Act, still limited immigration to only 105 people a year. At least until the National Origins Act of 1924 which then effectively ended Japanese immigration, the number of Japanese immigrants increased in this period where Chinese were not permitted entry. I bring this up just to mention that there were pretty strong limits put on Chinese immigration until after well the Korean War came to an end. Maybe worth mentioning is that a contributing factor to the repeal of the Chinese Exclusion Act was China's role as a member of the Allied Forces in their fight against Japan in WWII/SJII.
All that said, I've never encountered any documentation that such Chinese internment camps ever existed in America during the Korean War, even in circles with more radical interpretations. So, no, not that I've ever seen mentioned in any sources whatsoever.
No, they had the Red Scare instead. The enemy wasn't perceived to be the Chinese. The enemy was perceived to be "The Communists".