It is better to turn these properties to a professional property manager who carries high insurance coverage.

You do not necessarily need to anything special with registering it with the state/county just get it prepared from a rental perspective (enough towels, dishes, etc) and I would talk to your insurance company to adjust coverage for a little more liability and overall coverage.

What is the best type of insurance coverage for this situation?

If you do that, I would suggest that you max. out the liability coverage on your landlord policy and follow it up with an umbrella for 1-5 million. 

The coverage will not be standardized like a homeowners. 

As the region is bracing for a big one, should I be getting earthquake coverage for these investment properties?

You should still be able to deduct interest and property taxes as a business expense on rental properties.4) There are provisions allowing for accelerated depreciation and limitations on interest expense for businesses though it is not clear how those will be treated within the real estate space.Generally speaking, most of what you see as generic news coverage is going to discuss the impact on individual tax returns. 

Most likely the seller will not cover agent's fee so you will need to put that on the top on your purchasing price.

If you know of any brokerages with a flat fee per transaction or 100% commission, maybe a monthly fee, set annual fee for E &O coverage, then that is something I would be interested in checking out.

And also look at "Loss of Rental Income" coverage in case something claim related happens and the tenant has to move out you'll still be able to collect the lost rent while repairs are being made.