I think items 2-5 are implications of #1: stay focused. My previous startup probably had a similar grand vision as Precog, but we decided to focus on a specific use case (credit card fraud) first. Even still, we found fraud was itself a broad problem with several subcategories; techniques that work well for an online marketplace for vacation rentals might not work for an e-commerce shop that sells shoes.
A template that I love is the one from Crossing the Chasm:
For [Target Customer] who has [Problem], our product is a [New Product Category] that provides [Key Benefit]. Unlike [Competitor], we have [Key Point of Differentiation].
Two declarative sentences. Sounds easy, but few startup founders succeed at this exercise the first time they try. However, once you can do this, just about everything else--selling to customers, convincing talented employees to join, raising funding from VCs--becomes vastly easier.
I wish more startup advice focused on basics like that.