How do you define yoga, yogi, and yoga teacher?

As per my opinion.

Yoga is a supreme science.

Because yoga will activate every organ in your body and it will make function properly.

And also yoga has energy to cure some disease.

And coming to Yogi means 

Who practices yoga regularly with conscious awareness on breathing.

Coming to yoga teacher.

Who have utmost knowledge on yoga and have capability to teach others in a healthy way.

Hope my answer will give you a way to start yoga.

Thank you.

Yoga-->word 'Yoga' is is dervived sanskrit root word 'yuj' which means to join or unite. Which means connecting our mind body and soul.

Yogi-->One who is practicing yoga and and adapting yogic lifestyle.

Yoga Teacher--> One who teaches yoga and yogic lifestyle weather he teach how to perform asana or detailed knowledge of asanas, pranayams, mudra, dhyan, dharna, samadhi and other forms of Yoga theortically as well as practically.

Yoga is a way of life.. Yoga means unity- unity of mind , body and soul.

Yogi is someone who practices yoga.

Yogi is often referred to male. Yogini for female.

A yoga teacher is an individual trained to properly teach the poses used in yoga practice. Their role can also extend beyond the physical aspects of yoga as they may take a holistic approach that incorporates the mental, emotional and spiritual elements of the discipline into their teaching.

Yoga is a science of physical and mental and spiritual fitness.

Yogi is a person who learn yoga philosophy and asanas and pranayam from yoga class or under guidence of yoga teacher.Yogi is self disciplined 

Yoga Teacher is certified tutor  a Guru of Yogi who teaches yoga poses and pranayam to him.