Legal Question in Real Estate Law in California

Of course they can, just like the holder of a home equity loan can foreclose if you don't pay them even if your first mortgage is current and just as the County Assessor can foreclose on the tax lien if you don't pay your taxes regardless of whether you are current on your loans. They are totally separate obligations and separate liens on the property, each of which can be foreclosed on without regard for the status of the other debts.

Yes. It's a different kind of lien from a "mortgage" or a deed of trust, but also subject to foreclosure, as are judgment liens, mechanic's liens, and tax liens.

Of course. HOA liens can be foreclosed and so can mechanic's liens.