Can these be easily arranged without a car? Where would you recommend if one wants to see "traditional Korea"? Thanks in advance.

LAX

This might be a good idea: http://www.koreanfolk.co.kr/
It's a traditional Korean folk village, built outside of Seoul. I was there in the late '90s, so don't remember every detail, but you can walk around this really peaceful setting and see traditional village architecture (how all homes were built with heating systems running under the floorboards, etc.)
There are some cool activities to watch - folk dancing, a traditional wedding, etc.
And I also remember seeing a bunch of international visitors there; I think a lot of them were American soliders based in Korea.
And you can get there by subway/bus, if memory serves.

If you don't have much time the Folk Village described by lombardo is a good choice. But if one day in Seoul is enough for you, please check tours to Gyeongju in the SE between Daegu and Busan. A bad comparison, but it could be called "the Kyoto of Korea".

Does any one know a good place in Seoul for Akasuri (I don't know the Korean word, but it's sometimes called red scrub in English).

I've lived and traveled in Asia for over 30 years and never considered Seoul as a 'tourist destination' stop....this is not a knock on Korea because I thoroughly enjoy all my business trips. Even my local friends and business associates agree with me on this :p

Koreans also have extreme difficult time speaking English and getting around requires a little bit of patience.