I used to have a really good lesson plan for APUSH on how the Korean War was viewed by Americans in the 1950's, but for the life of me, I can't seem to find the damn thing.

The long and short of it is that the Korean War is called "America's forgotten war" for a reason. Returning GIs desperately wanted to forget it - Korea's frigid winters, crushingly humid summers, and ubiquitous ridgelines coupled with the endless stalemates made for a very miserable experience. Most just wanted to pick up their lives where they left off and not dwell on their time in the war.

Furthermore, the Korean War was overall incredibly unpopular with the American people. While public opinion tended to fluctuate with how well the UN forces were doing at the time, it wasn't uncommon to see nearly half of Americans saying that going into Korea was a mistake or that it was going to lead to World War III. Polls conducted by the Eisenhower administration upon Ike assuming office in 1953 were particularly grim: over half of Americans thought the war wasn't worth fighting, and a vast majority just wanted an armistice as soon as possible.

In short, no to both on your questions. The end result of the Korean War was that Americans wanted nothing to do with Korea and wanted to forget about the place as soon as possible. (This even extended into academia - the study of Korea as an academic field didn't really begin until the 1960s, when Edward W. Wagner, James Palais, and Gari Ledyard more or less founded Korean Studies in the United States.)

The Korean War resulted in the exportation of one thing: people. Immigration law was changed in 1952 which removed some racial restrictions and allowed GI's to bring back foreign wives and children. Holt International Children's Services was created in 1955 to help people adopt Korean War orphans, especially bi-racial children of Korean women and US soldiers. This article from Time has some good photos of orphans in the 60's and discusses the Korean government's racial views and plans to remove bi-racial children through adoption.

Further, while the Korean War ended in 1953, the US has maintained a sizable presence ever since then. From 1955 until 1970, there were between 50 and 70 thousand US soldiers in Korea at any given time. In the 70's, the numbers dropped to around 40k, and in the mid 90's, the numbers dropped to the mid 30's and finally in the mid 2000's to just under 30k. It's important to remember that these soldiers usually spend a year in Korea with the option to extend to a second year, so besides the soldiers who fought in the Korean war, the US military has rotated millions of people through Korea over the years.

Clearly with the exportation of people through war brides and orphans, and the rotation of so many US soldiers, there was some exportation of Korean culture. But I think it's all relative. Orphans don't take very much culture with them. Compared to the recent exportation of Korean culture via television dramas, K-Pop, movies, and technology, the amount of cultural exportation following the Korean War was a trickle.