Is it possible to do better than Cramér Rao lower bound for different estimation methods
Does the calculation of the CRLB imply that only particular estimation algorithms can be used (e.g. estimating delay and Doppler from a complex ambiguity surface) which satisfy the CRLB inequality? 


All unbiased estimators satisfy the CRLB. 

You don't, however, have to use an unbiased estimator. Biased estimators might be lower in variance than the CRLB would allow for a biased estimator.

The existence of the CRLB doesn't force you to use any specific algorithm.