No, Yes, No, No
Not sure why everyone is writing multiple paragraphs, you asked simple questions, these are the answers.
Maybe because they don't feel that just the answer, especially wrong ones really answer the question.
Plus the simple fact that it you read the question, it asked for elaboration.
: still maintain a selectable distance to the car in front?
No, this is a function of Traffic Aware Cruise Control (TACC) one of those items explicitly listed.
: still apply the brakes aggressively when something is in front?
Only emergency braking, the type that you never want to test.
: lane control of any sort?
You will not have anything controlling the steering wheel, but you will have the wheel shake when crossing lane inadvertently
: how about backing hazards.
You will have the close hazard lines. I don't think that a crossing vehicle in the back is actually warned right now anyway.
I have the 2018 Leaf with ProPilot, EAP provides the same functionality as ProPilot, but does it a LOT better. Whereas the Leaf will tend to turn on and off driving down most roads that aren't Interstates, the Tesla stay own the entire way. The Tesla autopilot does a great job of driving the car now. It's not perfect yet, but hopefully that isn't far off. It will now see a curve and slow down to a speed that is comfortable for the curve. At a full stop, like a traffic light, if behind a car, it handles everything, unlike Nissan where you have to re-enable most of the time.
Like the Nissan, the intelligent cruise control (TACC) is probably one of the best things that can dramatically reduce driving workload. Works awesome in rush hour stop and go traffic.
My recommendation, get it now, roll it into the loan, it's cheaper and doesn't hurt as bad when in a loan.
To me, the advantage of EAP is much more than AWD or the Performance model.