Legal Question in Landlord & Tenant Law in California

Yes, the new owner will be your new landlord, and is subject to whatever lease you have, the same as the previous owner and landlord. You should consult with an attorney to get more specifics.

Yes, you have the same rights as before the sale, and the same obligations. You are just trading one landlord for another. You should, however, make sure you know when escrow will close, and make sure the old and new owner and you have a clear understanding of how any partial rent will be handled if escrow closes mid-month. You also need to be aware that your old landlord might have been perfectly happy to renew your lease when it is up, or continue a month-to-month tenancy indefinitely, but they had the RIGHT not to renew, or to terminate the month-to-month with proper notice in some circumstances and to raise the rent provided it was within legal limits under LA rent control. So the new landlord will have those rights, and may exercise them to move into the house or otherwise alter the terms and conditions of your tenancy, or terminate it - if and to the extent allowed under the Los Angeles rent control and just cause eviction ordinances. For more information I suggest you contact the LA Rent Board and/or one of the numerous tenants rights organizations in LA.