Legal Question in Landlord & Tenant Law in California

The landlord's estate becomes responsible until a probate court decides who will get the property. You might contact the landlord's spouse or, if none, his children.

I'm not sure what you're asking by your second question, and can't even guess. The landlord can make rules for tenants, as long as they're reasonable, such as no littering or smoking in the hallways, no pets over a certain weight, etc.

Depending on what your rental agreement is, you might be responsible for paying the waste collection company. You should be able to negotiate that with a landlord (or his/her representative) if you're entering into a new rental agreement.