Based upon the information you have provided, you may very well be entitled to spousal support and/or alimony. The duration and the amount of the support payments is usually determined by the court, based on numerous factors. You may want to contact an attorney, just to make sure that you are not waiving any of your rights.
This is not simple and may require some additional information before the answer can be given. Generally, one cannot just give away his parental rights. It could, for example, be possible to give up parental rights when another person is adopting the child. In any rate, a person cannot simple terminate his/hers parental rights in order to avoid paying child support.
Although the best interest of the child is the standard applied in custody cases, there are many factors that may play into the situation. An experienced attorney should be able to help you with filing for custody, while your divorce is going on.
PFA and custody proceeding are not one of the same. Although, PFA can include some temporary provisions regarding custody, it is often anticipated that a subsequent custody proceedings would change that. In general, I agree with my colleagues who had already responded to your question.