Are all yoga teachers in gyms part-time? Can they be full-time?

They are usually part-time, but there are also full-time yoga teachers, but there are fewer of them. Generally speaking, they have another job, because this way they make money faster, and the wages of part-time and full-time teachers are actually the same. It won't be much different, it mainly depends on your performance. If you are good, your salary will be better.