Question

upto what extent electric field inside a conductor is zero ? is it depends on size of a conductor?

Answer 1

it does not depend on the size of conductor
no matter what shape or size a conductor have, the field inside the material will always be zero....

Answer 2

in that case what happens to electrons in the conductor if electricfield is very high to oppose?

Answer 3

under VERY high field the capacitor may get discharged