You can't get a green (yellow) based budgie from mating an albino to a type 2 yellow face but you may get a yellow face bird that looks greenish. The yellow would be a lighter shade than the yellow on a normal green and the body colour would be an indistinct greenish shade of blue.
Your second question about the yellow face is possible. If the mother has a white face but she is a double factor type 1 yellow face all her chicks would be type 1 yellow face but as the dad is type 2 yellow face half of the chicks would also be type 2 yellow face. The chicks that had both mutations of yellow face would just look like type 2s. If this is the case with your pair then there would be no white face chicks. A lot of type 2 yellow face birds look like type 1 until they moult