what effect do the excecutions and the ban on singing Beast of England have on the animals ?

The animals are rules by Napoleon who rules through fear and nothing else. As he changes the society to be the way he wants it to be, taking away anything that might help them to think for themselves is one way to control them. If the executions continue, the animals will be cowed into submission, never questioning Napoleon's rules. Further, Beasts of England is now from another time, a time that Napoleon does not want them to think about.

It certainly destroys the original spirit of the revolution. The effect is very similar as it would have been with people in say Stalinist Russia. The animals are scared to say or do anything that might be interpreted against the new ideology. Inside they are terrified and confused but Napoleon's autocratic farm-state is too intimidating to say or do anything to the contrary.

The animals are completely confused by the bloodshed, the inquisition, and the executions of the animals by the dogs. Boxer thinks it must have been their own fault, that the executions were enacted because they must have done something wrong. He resolves to work harder, and in turn the other animals seem to follow suit. Whether it was really guilt or basic feelings of terror the result is the same; everyone goes back to work, the rations get smaller, and things could not have been worse.