Tan Jan Oh are breathing exercises. They are done for many reasons - breath control, pain control, stress relief, Ki development, plus they help greatly in warming up.
Kicking is an integral part of Hapkido. Although probably known more for its joint locks, the art has a great variety of kicks, even more than Taekwondo. Shown are a few different ones from the standard front, roundhouse, & side kicks every art seems to have.
Punching and hand striking techniques exist in Hapkido, but are a minor part of it. Better is to use techniques that give you control of your opponent.
I am a very hands-on teacher. I believe that to understand a technique, you have to feel what it's like on the receiving end as well as the giving end.