Congratulations on the P3. It's a fantastic start.
Everything you need to know to get started can be found in the owners manual. If you don't have one, you can download a copy from the DJI website https://dl.djicdn.com/downloads/phantom_3/User%20Manual/Phantom_3_Standard_User_Manual_v1.4_en.pdf
I think I paid around $600 for my P3P just a year ago. It was new. If it's never been activated, there is a slight chance the battery may have gone bad. You could always test the battery by attempting to charge it up.
State Farm does not offer "drone insurance" of any kind. It's called a personal articles policy and covers a wide range of property, including cameras. A claim will result in a payout, however, you will most likely not get renewed and/or your rates could increase regardless of insurance company...
Good point. I purchased several a couple of years ago at a low price from Target. On the advice of some other more experienced pilots I placed them into rotation with my older batteries rather than place them in storage.
As stated earlier the difference between 1080P and 2.7K is discernible. Likewise, I find the difference between 2.7K and 4K also discernible.
Sometimes people looking for "quality" are really after a different look. Are you happy with the picture style?