1) The technician was expected by the doctor to develop the X-rays fast.
But I would remove 'by the doctor' and 'by the technician' in this and the other examples.
2) It was expected by the doctor that the technician develop the X-rays fast.

3) The doctor expected the X-rays would be developed fast by the technician.

4) It was expected by the doctor that the X-rays would be developed fast by the technician.

The 'would' is what is missing from 2)