Well you can’t serve someone with separation papers. You can give them to him. He doesn’t have to sign them. He probably won’t if they are not in his favor.
Most (not all) attorneys require retainers. All will require a initial consultation fee. It is their livelihood after all.
Leaving the house does not “look good”.
“3. Do not move out of the marital home without talking to an attorney first.” (Rosen.com)
The only way to get custody of your daughter is to sue him for custody. That takes money (i.e. a lawyer). Yes you could do it by yourself. Typically those don’t turn out well. I assume there was no abuse either of you our your daughter.
Without custody you will have to pay child support. It matters not if you can’t afford it. It is calculated on your gross pay. Expenses do not figure in unless they are other child support expenses.