The ISS would be absolutely worthless as a tether for a space elevator, not enough mass to be useful. Not to mention the fact that the anchor for a theoretical space elevator would have to be well past Geosynchronous orbit. The CG of the elevator needs to be at GEO, not the end of it.

Sending someone suborbital isn't quite the same as a multi-day orbital trip to the ISS.

ISO 9000 and ISO 9001 are not limited to the government. There are many industry standards regarding record keeping and paper trails of critical hardware.

SpaceX has developed their own engines. 4 at last count: Merlin, Merlin Vac, Kestrel, and Draco. They are using common dome tanks, which NASA (as far as I know) is not using in their current programs. SpaceX started as little more than an assembler of outsourced and off the shelf parts, but these days they pretty much design and build as much in house as they can. They may be relying on a lot of NASA's theoretical research of years past, but they are definitely designing their own rocket rather than just slapping NASA parts together.