I have completed the diversion program, and would like to know how long it takes until the charges are withdrawn. Also, I am wondering if the police can still have access to the fingerprints and records of the proceedings. If I ever get pulled, can the police see the offence and that the charges dropped due to the diversion?

You have to stay out of trouble for so many years and meet any conditions they give you. Even then they stay on your record but can't be acessed easily by just anybody.
Technically I don't think the charges are dropped because you went to diversions but they are reduced and/or satisfied.