No they have no legal authority to do this. Only a court may order deletion of images.

PCSO's have no such powers, and police do not except in specific circumstances. But you may save yourself from being arrested if you comply.

In certain circumstances, yes, but note that all these powers are restricted to police, not PCSO's.

They can ask but you are not obliged to answer them. However security is their job and whether or not their questions seem daft you would be wise to explain in polite, non-confrontational terms.

In public places where there is no right to privacy, yes you can.