Can I File For Child Support While My Baby's Father Still Rents A Room In My Apartment? Location: California

Location: California

I am currently 37 weeks pregnant with my first child. The baby's father and I are no longer together, and he recently decided that he does not want to be involved in our child's life. I'm planning to file for child support shortly after our daughter is born in November, which he is unaware of...

Unfortunately our living arrangements make things a little complicated...

We currently live at the same address, but we are not in a relationship and he intends on moving out within the next couple months. He and his brother occupy the second bedroom of my two-bedroom apartment and pay rent, while I occupy the primary bedroom; I am the only one actually on the lease. He and I previously shared a room with his brother in the second bedroom, but that has since changed. We now have separate living arrangements, and I will be the baby's primary caregiver. He has expressed that he does not want to be on the birth certificate and does not want to have any involvement with the baby.

The father plans to move out, but the timeline is uncertain. We've discussed him remaining until I return to work from maternity leave in February as I will have a more steady income, he will have time to find another place, or I will be able to downsize without having to pack up my apartment immediately postpartum. However, I would prefer to establish paternity and child support as soon as possible rather than waiting until he moves out.

My main questions are:

1. Can I even open a California child support case while we technically still share an address? Will DCSS consider us to be living together as a family even though we're separated and he is essentially renting a room and not contributing to parenting time/childcare(He is now never home, often leaving the apartment at around 10/11am and not returning until 4am)?
2. Does his paying rent affect child support calculations? His payments cover his and his brother's living arrangements, rather than being a direct contribution toward expenses for our daughter. But will DCSS/the court see it that way?
3. How is parenting time calculated when parents share an address but don't share childcare? I expect to be responsible for nearly all of our newborn's daily care.
4. What does the timeline generally look like? If I file immediately after my baby is born, how long might it take to establish parentage, obtain a support order, and begin receiving payments?
5. If he moves out while the case is pending, can I update DCSS? Would that change how the initial support order is calculated if his rent contributions were considered before?
6. Would it make sense to establish parentage through a Voluntary Declaration of Parentage (VDOP) at the hospital if he's willing to sign? Would that meaningfully speed up the child support process or should I just go the route of establishing through the court rather than trying to persuade him?

For context: We are unmarried. I can likely afford the rent on my own should he decide to leave immediately but money would definitely be tight on my disability income alone. I have my own income and plan to return to work in February, but will have to penny pinch until that time should he leave immediately. I am not asking him to support me personally. I'm just trying to establish appropriate financial support for our daughter.