If my son's mother is harassing me (by phone, calling and texting, calling my job, showing up unannounced at my home & job) can I file harassment charges or a report on her, and also can I nor our son have no contact with her until we go to court for custody/visitation?
It is not clear from your question what your options are. What does this "harassment" consist of? Threats? Stalking? Or just being a nuisance because you don't get along?
If the "harassment" is truly frightening or extremely annoying (odd hours of the night, perhaps the showing up at your job, repeated telephone calls), you might be able to get an order of protection, and if the behavior persists, seek police intervention or court contempt/violation proceedings.
I take it you have de facto physical custody of your son because the mother has so far "abandoned" him to your care, but have not gone to court yet to establish that you have legal or physical custody and some sort of shared parenting plan or schedule for the mother to have visitation or shared parenting? I would certainly consider doing this as soon as possible, and looking into a Family Law attorney in Onondaga County to assist you.
Getting court ordered and approved arrangements may help to stop or moderate this harassing behavior of the child's mother you are complaining about.