Legal Question in Landlord & Tenant Law in California

Check your lease. If its even half-decent it says that only tenants and listed residents are allowed to live there. So you are entirely within your rights to require her to qualify as a tenant and pay a security deposit if she is going to live there. Or you can just refuse to allow her to live there, and have her removed by unlawful detainer if she doesn't leave.

As for the dog, if it says no pets, even a tenant can't just suddenly bring in a service dog. A non-tenant certainly can't. A tenant must request a "reasonable accommodation" and provide confirmation from a licensed health care provider that either a trained service animal, or emotional support animal is necessary to the tenant. False representation that an animal is a trained service animal or that a person has been prescribed a service or emotional support animal is a misdemeanor punishable by upt to $1,000 fine and up to six months in county jail.

If she does have proof she was told by a licensed professional that she needs the dog, however, and you accept her as a tenant, you cannot ask for any extra security deposit for the dog, even if you could ask for an extra deposit for a regular pet dog. You can only require the same deposit as any other tenant.