a) No, it is not true that E[delta prime|delta=theta]=0 for all theta. The LMS estimator minimizes the mean squared error, but that does not guarantee that the conditional expectation of the estimation error will be zero for all values of delta. In other words, while E[delta prime|X=x]=0 for every x, it is not necessarily true that E[delta prime|delta=theta]=0 for all theta.
b) No, the property Variance(delta)=Variance(delta hat)+Variance(delta prime) is not true for every estimator delta hat. This property is specific to the LMS estimator, which is designed to minimize the mean squared error. Other estimators may have different properties and may not necessarily follow this equation.