And as others said, see how having dogs on the property might impact your insurance coverage.

Is the lack of coverage spelled out in your policy?

This is great news for those properties that are in the high-risk flood zone, I would suggest that you do two thing flood mitigation (comes in many forms and sometimes you can get access to grants and loans to do the work) and transfer your risk through insurance, just make sure you are working with someone who is savvy in the emerging private flood market and NFIP you don't want to overpay if your agent writes the policy incorrectly and you don't want to buy a policy that an agent that doesn't specialize in flood insurance might sell which sounds good on price but really isn't coverage that will get you back to whole.Last note every community has a FLOODPLAIN MANAGER a government job, I would suggest if you are going to do any mitigation work get their thoughts and council, they can also offer resources and contractors or surveyors that can make sure your mitigation is doing what you want that is routing the water away from your structures.   

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.