A: It depends. If you are going to file against a City or County, then you typically have to give them notice and it must be done within a certain time frame (and its not very long) and in must be in a certain format. In terms of suing a person, it depends on the person and what you are suing for. Some statutes require advance notice for some causes of action. You will want to seek the advice of counsel to ensure you are doing this properly, and within the time framework required, or you may be prohibited from bringing the claim.
A: You can file a Request to Modify Support and Visitation, and also bring in the Dept of Child Support Services (they normally coordinate guideline support payments upon delegation of the court). That will help you get an increase in support from the date of filing into the future. There are judicial counsil forms available at courts.ca.gov/forms. You should get help from the court family law self help, private counsel or a certified family law paralegal to ensure that you have filled out the forms properly and/or attached the pertinent documents.
In terms of the arrears, you can bring the issue up with Dept of Child Support Services and have them help garnish wages.
A: If there is a restraining order in place, then make sure you do nothing to violate those terms. Violating the restraining order will not support your efforts to be more present in the child's life.
If you believe you are the father of the child, you can file a petition in family court for a declaration of paternity and obtain verification that the child is yours. Then you can request visitation and other rights to see, and support, the child.
Many courts have family law self help clinics to assist in the preparation of the relevant forms.