California owners, should we increase our coverage, which should result in higher premiums?  

You're a business owner now nothing wrong with that.   

There are some amazing physician loans available that can allow you to purchase a owner occupied single family property with 0% down. 

This vary heavily town to town. 20% down is great if buying strictly as investment but if you have a way of owner occupying I would explore that route and apply the 20% down to increasing value of property and instead using low money down loan. 

I noticed that the previous owner let them pay half the security deposit and the other half later, which is a red flag.

Handle this promptly to protect the owner’s interests.

I got from this LP the name of the owner of 711Rescue: Zak Shaik.

The squeaky wheel wins in development so I'd recommend you staying on all communication with the city so that you can see the communication and push as the owner.

Buyers don’t care if you shelled out more on the rehab, if you’re priced too high, you’ll end up sitting on the market way longer than you want, driving up holding costs.Lastly if your buying on market, REO or Corporate sellers are dominating and not as willing to negotiate as owners would.

Can you reach out to their owners and see what they’re doing?