// Unlocking the doors...
The reason they auto-close again is (presumably) because with a remote control it's very easy to accidentally unlock either with the keys in your pocket or because kids are playing with them. You don't want the car parked unlocked all week w/o you knowing if that happens.
// Closing the trunk
I think this is a combination of "why is my rear hatch door automatic now" and "why does it move slowly." The answer to the former I think is so you can open your trunk remotely and then grab and carry the stuff, and also to enable the short/weaker folks to operate the taller hatch door (vs a lower-trunk, which isn't what you have...) And then the reason the automatic hatch closes slowly is to not injure you or your child if you happen to not get out of the way quickly enough.
// Starting the engine
I think that audio-ding exists to alert you if a child has touched the start button, which they can obviously do with key-less ignition.
// Using your turn signals
This is the one that sounds truly wrong - if your car alerts you of adjacent vehicles when it shouldn't, (a) you can probably turn off that assist and (b) you should tell the company because it literally sounds like a bug.
// Coming to a full stop
Ditto for hands on the wheel during stop - sounds like a bug.
// The goddamn tires themselves
Yes sounds like you have flawed pressure sensors, go take the car to the dealer.