If my kid’s father and I have joint legal custody and I have full physical custody, is it mandatory for him to know the school address and my home address?

I am not aware of any reason why you would have to disclose your home address.  You don't HAVE to disclose the school address, but the father will have equal access under law if he chooses to reach out and get it (See state law posted below), so I don't see any reason why you should withhold the school address. 

If you are concerned about your safety or your child's safety, then you should really get a restraining order. 

You should also speak with a family law attorney about whether or not you should be receiving child support.

Best of luck.

Ed Code 49069.  Parents of currently enrolled or former pupils have anabsolute right to access to any and all pupil records related totheir children that are maintained by school districts or privateschools. The editing or withholding of any of those records, exceptas provided for in this chapter, is prohibited.   Each school district shall adopt procedures for the granting ofrequests by parents for copies of all pupil records pursuant toSection 49065, or to inspect and review records during regular schoolhours, provided that the requested access shall be granted no laterthan five business days following the date of the request. Proceduresshall include the notification to the parent of the location of allofficial pupil records if not centrally located and the availabilityof qualified certificated personnel to interpret records ifrequested.