That is in CA, no earthquake and not in a flood zone.

Don’t know about masonry in earthquake country, but there are entire communities of these homes, built in the ‘50’s, that are very popular here (and apparently still standing).

During an earthquake the house became damaged and new city ordinances prevented them from rebuilding the house and they still owed on a mortgage for the property so they were on the hook for the mortgage but could not use the land or live on it anymore.

In working with insurance companies I've found that they rarely cover mold issues as they consider it long term or chronic in nature and their policies generally only allow flames of acute or emergency situations i.e. plumbing breaK or leak, wind, fire, tornado, earthquake, hurricane, etc.You may think it's a good deal now but once you start digging into it it's like a dentist digging into a cavity.

This is coming form the ASCE design manual for concrete structures related to zones prone to earthquakes...

The neighborhood borders very upscale Miami Shores and rapidly gentrifying Little Haiti.

Do I need separate earthquake insurance in SF?  

Personally I'd prefer hurricanes over earthquakes or tsunamis.

Due note that if you're going to finish the first floor, it's a great time to add earthquake anchor bolts to the foundation if you wish, add drainage to a concrete backyard and garage if there isn't any yet and update/add to the existing plumbing and electrical (also add Ethernet and new cable) before all areas get enclosed with Sheetrock.

If you're going the umbrella insurance route, make sure it will cover you for several things including just the routine slip and fall (like mold or earthquake).