1 - This is a world where you can bioengineer dinosaurs. It stands to reason that their car technology is also more advanced.
2 - Before the i-Rex escapes, Claire is updated on the status of a pachycephalosaurus (the ones with the bone bulb-like thing on their heads) who had lost her tracking device. Or maybe it was the i-Rex doing random things and moving back and forth, testing the world and exploring what she could do. Or maybe any other incident, because in real life not everything that happens need to be related to the main plot, and that would make JW cinema verite.
3 - Hubris. They never dreamed things could ever go this badly, so their security was lacking in every area. Also, it’s still a business, lowest bidder and so forth.
Nice. The assistant was symbolic of the emotional change in Claire. Even if the writers weren’t conscious of what they were doing that’s probably what was in the back of their minds.