I want 100% legal and physical custody of my 9 month son and the father is willing to sign the papers. Can I still collect Child Support, or since I am getting 100% legal custody the parenting agreement is done and the father gets to walk away?
You are confusing custody with support.
You also don't want to forget visitation.
Just because dad stipulates and agrees that you get 100% custody, doesn't mean he can't (or won't later) seek visitation.
The custodial parent is usually entitled to receive child support to assist in caring for the child.
I strongly suggest you don't do anything until you meet with a couple lawyers about this.
You don't have to hire those lawyers, just meet with them to discuss the basics of child support, child custody, and child visitation in your county and state.
The initial meetings are often free of charge and/or obligation.
I see you are in California.
All states will assist a parent in establishing child support payments and paternity.
Has the "dad" established his paternity via DNA testing?
Signing a birth certificate isn't ironclad, because "dad' can later seek paternity testing and have the child support encumbrance removed should the DNA prove him NOT to be the "baby daddy".
I suggest you educate yourself about the entire process in your state:
http://www.childsup.ca.gov/Default.aspx
http://www.childsup.ca.gov/Resources/ApplyForServices.aspx
http://www.cadivorce.com/california-divorce-guide/child-support/
https://www.cse.ca.gov/ChildSupport/cse/selfService/participant/notLoggedIn/home/welcome
This is a useful child support calculator. It will help you determine how much the law will allow:
http://www.alllaw.com/calculators/childsupport/california/