I am not in CA, so I am not sure how CA's real estate law requires. Normally, title company will do a title search to recover the history of the title of the propety, and your attorney should read the abstract of the title to determine if the title is clean. This is not only if the title is lien free/clean, but if the seller has the ownership of this property and what kind of owndership it is. However, no matter how complete research and review, no one could gurrantee no title issue later, so the standard method for residence property is to buy a title insurance and title company will be responsible for any title issue in the future (exceptions are defined by law).
Title search need to check the public records in the county's office. However, if the lien filed recently and had not been recorded for public , the title company might miss the lien; some other cases such as law suit might impact the the title.
I wonder why these two questions need your answers, these should be questions for seller.
You agent has no obligation to answer any questions about title because it should be prohibeted by law. The standard answer from an agent might be asking your attorney, and remind of your buying a title insurance.
