I'd be interested to know whether the following rationale matches the way you'd choose between "stand" and "lie" in Danish. My guess would be that it does, since language flows from human thought.
My understanding of these expressions is that the object is being anthropomorphized. The aspect ratio (tall and thin, short and flat, or square-shaped) of the object *as placed* (so, not necessarily its normal intrinsic shape) determines the corresponding human attitude used to represent the object. There is some wiggle-room. The limousine is flatter than it is tall, but it's not as flat as a sheet of paper, so I'd be happy saying that a limousine is either standing or sitting outside, but not lying. Let's take the example of a phone, if someone says "sit/lie your phone on that table," then that would sound fairly normal (although "put" would be even more normal) and I'd place it down flat. If they said "stand your phone on that table" then that would sound unusual, and I'd probably try and stand the phone on end if I were feeling cooperative enough. A vase can sit or stand, but most vases are taller than they are wide so "stand" would be more usual for such a shape. As I say, there's wiggle-room for objects with aspect ratios close to 1, so even in #5 you could use "lie". But be aware of "lie" versus "lay". You can either say
"Today, on the bench, lies a watermelon."
or
"Yesterday, a watermelon lay on the bench."