Probably. With a car tire at ~30psi and the cable thin enough that the tire can conform around it, the force squishing the cable is likely less than from a person stepping on it.
But, very interesting to explore experimentally!
that sounds like an interesting experiment, especially if you were to try say a light small car versus a bigger pickup and measue before and after throughput
"It depends..."
If any of the conductors break, no.
As long as continuity is maintained I... don't know. I haven't done much with 5GBASE-T so I don't know how much headroom is built into the spec. Gut guess would be you can.
One way to find out!