how does door lock

That is just the way they were made. By holding the button in you are putting things into a bind. The door unlocks when you close it, but pushing the button prevents the lock button from popping up to signal that is in fact unlocked.

And yes the drivers door is the only door that will unlock and open from the inside by just pulling the inside door handle. These are old old forgotten design features that chrysler thought up way back then.

No you misunderstood. I shut both doors and lock the doors with a key standing outside the car. When I use the outside door handle the car opens and as I push the button on the handle the black button inside the car pops up and in you go.