Can a police officer give a lesser charge if suspect make a statement?

The officer can only make decisions on whether to arrest, cite, or not to arrest, referred to as officer discretion.

The officer cannot (honestly) promise leniency of a charge because they do not have that authority. Charges are filed and issued by a prosecutor, not a police officer. Any statements given to a police officer based on a "promise of leniency" without the prosecutor's cooperation will be considered coerced and inadmissible.