Certain beyond reasonable doubt. Let me first say that the cosmological constant is not a model of dark energy. The cosmological constant is a low energy, effective description of whatever dark energy really is.

Dark energy is the term coined to describe the accelerated expansion of the universe, most people (myself included) believe that this is due to vacuum energy. The quintessence story is a way of explaining the expansion, not as vacuum energy, but as interactions with a field. This field violates basically every single reasonable expectation (that's why not many people like it) and (to my knowledge) it barely works even in the simplest situations. If the expansion of the universe is due to a field like in the quintessence story, then it's possible you could something with it. However, you will struggle to find a single researcher that believes the expansion of the universe is due to something different that vacuum energy.

So just to put a bit of salt on it. My answer was regarding the energy of empty space. I believe that beyond any reasonable doubt dark energy is the energy of empty space. If this is true, there is no way to make dale energy BH. On the other hand, if it turns out that the universe expansion is due to some matter fields then you could in principle build stuff with it (like BH).

Yes. the maths is pretty straightforward, fields are the fundamental stuff and we see particles when these fields are excited.

Long story short, no. Dark energy is the energy of space itself. We cannot move it/compress it/manipulate it in anyway whatsoever. If I understood your idea correctly you want to put a lot of dark energy in a tiny space and see what happens. This is like asking if you can put a big chunk of space in a little space.

I want to stress that even though dark energy is code term for "weird energy of empty space we don't understand anything about" by its very nature, it cannot be manipulated and hence dark energy BH are simply not possible.

I strongly disagree. "physical things" are precisely "observational quantities" and entropy is just as real as temperature/pressure or whatever thermodynamical quantity.

Going back to OP's question. The only physical law that differentiates past from future is entropy, all other (fundamental) physical laws are time reversal invariants. Many people believe that the passing of time is how we experience a gradient of entropy (Hawking has a beautiful argument of why the only way we can remember something is by increasing entropy in his brief history of time, I can find the exact part if you are interested). From this perspective, it is not that it just so happens that entropy increases with time, it is that we can only remember stuff with less entropy and the stuff we remember is what we call the past.