Is it possible for orthodontists to tell, by your teeth structure and size, when you will start your puberty growth spurt?

No, but other signs: The size and structure of the teeth are unrelated to puberty. X-rays of the wrists can be read to determine when growth will stop, but i know of no signs that puberty will begin other than growth spirt, change of voice, hair growth on face and around genitals.

No: I think physicians may give you a better idea of how you are progressing with respect to growth.

Other signs: Not structure and size, but timing of eruption. Actually, it's the other way around. Skeletal changes usually proceed dental changes. We expect to see specific changes in the dentition based on what we see as far as crank-facial maturation is concerned. Remember that the incisors and 6 year molars actually start to develop before birth, and the size of all teeth as determined before they erupt.