Your question does not disclose your home state. You should speak to an experienced local family law attorney about your options and what the fees will be. If you cannot afford an attorney, see if your local legal aid foundation, or a local law school has a family law clinic that can help you. Your local courthouse or battered women's shelter may also have a self-help clinic or be able to direct you to one.
The fees charged by attorneys (and most other professionals) are not set by law. Some attorneys charge significantly more than others. Some attorneys take longer to work through a case than others. That parties can make all sorts of unreasonable demands and thus drag out the proceedings.
Thus, how much the proceedings will cost cannot be accurately said.
The no contact order likely does not prohibit the parties from contacting each other to resolve their legal proceedings.
You likely should consult an attorney to review your no contact order and other facts to review your options.