Russ, so from my experience, here are the answers to your 2 excellent questions.
1. It shouldn't matter if you just purchased the property. Underwriters may want to know if there were prior losses if previously insured. For instance were there multiple water claims, so that they'll know if there's a mold exposure. However, a property not being previously insured should not stop it from being able to be insured now.
2. There are several different types of loss valuation available for property insurance. What you choose is important as it drives the rates used, the markets available, and the underwriting. All of these determine the premium, in addition to other factors like the Construction, Occupancy, Protection and other Exposures.
The valuation methods are:
Actual Cash Value, Functional Replacement Cost , Replacement Cost . These options are not all offered by every insurance company, or agency. Some Agencies may not sell ACV policies as they've had problems at the time of loss.
Actual Cash Value or ACV, is literally the depreciated value of the property. This will almost always be too little to rebuild the insured property with like kind and quality.
Replacement Cost however give the policyholder, subject to coinsurance provisions, the ability to rebuilt with like kind and quality, subject to the limit of insurance, for covered causes of loss.
Functional Replacement Cost provides the ability to rebuild, subject to coinsurance with a structure that will perform the same function, but may not be of like kind and quality.
Replacement Cost values themselves are derived using appraisal software by your Agent and the Insurance Company, or an appraiser, but they are not market value estimates, they are reconstruction cost estimates. In the Hudson Valley a builders grade type home in the finished areas would generally have a replacement cost of $200.00 per square foot. Less for basements that aren't finished, garages, and decks.
So, to summarize, there are various ways to value a property like that and the way you choose varies with the insurance company and how you want to be paid if there were to be a loss.
Thanks,