To the first question "why are you living?", I think you are living because you have no choice. Your parents brought you to the world and you have to be here. You can't just refuse to come to the world. 

To the second question "are you just existing or are you living with a purpose?", I think it may appear that you are just existing when you are bored or when you don't know what your life goal is, but your existence in this world has its meaning: to be loved by those who love you. Imagine what suffering your loved ones, your family would endure if they lost you. So let alone other magnificent purposes you live on this world like to change the world, to cure all diseases, to be loved by those who love you is the basic purpose. 

I like Yoga too. I go to the gym to do yoga three or four times a week with my friend and it's been almost a month. It was painful in the beginning because it hurt everywhere and I felt like the pain was going to kill me. But after several times, I started to enjoy the pain and now it doesn't feel like it's pain to me at all because it's an enjoyment instead. My muscle is still not that flexible and I still have a long way to go. But I enjoy doing yoga and I think if you really enjoy doing something, that's when you start to improve. Good luck to you!

Min