Dojang is the common name used to describe a Korean martial arts training hall / school.
Taekwondo
It is an South Korean martial art/sport
No one "assigned" taekwondo as a Korean martial art. Taekwondo was developed by Koreans for Koreans in Korea.
There is no established Korean Martial Art called "deon." The closest term I can find to this spelling of "deon" in Korean is 던져 (deon Jye) which means "throw" or 던지기 (deon ji gi) which means "to throw." Therefore, itmight be a technique, and not a Martial Art. I am not aware of any other such term in Korean by this spelling (perhaps an alternate English spelling would render a different Korean term).
Do jang is a Korean term. It refers to the school where the martial art is taught. In Japanese it is a dojo.
Tang soo do Hapkido Tae Kwon Do
No. Korea does have a similar martial art, but Aikido is Japanese.
Taekwondo
The Korean term for knife hand is "sonkal" (손칼). It is a hand technique commonly used in martial arts such as Taekwondo.
one martial art form was called tung soo do(not sure of spelling) a form of Korean karate
There is no actual known founder of the Korean martial art Tang Soo Do, however the name for the art of Tang Soo Do was adopted by Hwang Kee, the person who founded Moo Duk Kwan.