In the ideal configuration, when you have single-triple-single bond, they "want" to be in the same line. A molecule where they are bles have more energy. (Imagine that it's like a spring, but don't take the analogies to literally.)
The molecules where the bonds have wrong angles usually have more energy and they end to decompose in other molecules where the bonds have the correct angles or they have other bonds. [Oversimplifying warning, Chemistry is more complicated.]
In this case, since all atoms form a ring, everything is symmetric within the plane so forces cancel out. So maybe it’s more stable than one would think, similar to cubane.
But upon further consideration , the potential energy surface may be more like a saddle point, with each atom having a stable local minimum in-plane but unstable local maxima perpendicular to the plane.
(I’m not a chemist).
The atoms must be in a minimum of energy. They always oscillate a little due to thermodynamic and quantum effects. If they are in a saddle point the molecule blends until the atoms reach a minimum, until the atoms rearrange themselves in a different molecule or until the molecule split. (Or until they react with another molecule ...)
I studied a little of Chemistry, but this is out of the scope that I know well. IIUC correctly from https://en.wikipedia.org/wiki/Cubane the stability of cubane is not due to symmetry. The stability comes from the fact that locally it looks like a alkane, i.e. a molecule with Carbon and Hydrogen that only have single bonds. They are quite stable, the most common example is gasoline that is mostly alkanes.
Double bonds are more reactive. For example vegetable oils (that have also Oxygen, not only Carbon and Hydrogen) may have or not have double bonds. The one with many double bonds become rancid easier. https://en.wikipedia.org/wiki/Rancidification
Probably yes, but there may be some additional rules. First you need an even number of Carbons, but there may be additional rules.
I have a gut feeling that in this case it's better if the number of carbons is like 4n+2 (i.e. even, but not a multiple of 4, just like 18 :) ). This rule is important when you have a similar structure with double bonds and Hydrogen. https://en.wikipedia.org/wiki/Aromaticity I'm not sure if it translates to triple bonds.
(Some handwaving: Here the pi bonds in the plane act like the H in the aromatic compounds, and the pi bonds perpendicular to the plane form an aromatic system.) (Note that handwaving is never a replacement of knowledge, so this many be very bad.)
I feel like a larger ring would immediately twist into some kinda figure-8 shape. I feel like this one would too, were it not laying on a surface. Actually I feel like the surface plays a major role in this molecule's ability to exist.
The orbitals of the pi bonds are probably in awkward angles resulting in ring strain, and thus instability. It can be explained by the antibonding orbital overlap of the pi bonds.
The molecules where the bonds have wrong angles usually have more energy and they end to decompose in other molecules where the bonds have the correct angles or they have other bonds. [Oversimplifying warning, Chemistry is more complicated.]
Some nice graphics: https://www.sciencedirect.com/topics/chemistry/triple-bond Perhaps the text is too technical, but the graphics are nice.