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Does it have/use emergency braking in case of danger, if you don't use self-driving?

Yes.

Yes but they are phasing out radar in favor of vision-only. Model 3 and Y have been shipping without radar braking for the past few months.

They still do emergency braking regardless of the sensor technology.

The vision-only system has passed all required tests for certification and Tesla themselves consider it to be a much safer system now.