That's pretty standard for experimental quantum systems. A lot run on helium fridges at 4K. The superconducting stuff even colder, in 10 mK dilution fridges.
1. The main underpinning of this article is the analytical theory they come up with independent of their simulation. The fact that it explains a few qubits well is exactly why this is interesting. If you were to scale up their model - a spin-1/2 ising model, you would effectively get a classical magnet, which is obviously well described by classical thermodynamics. It's in limit of small systems that quantum mechanics makes thermodynamics tricky.
2. Their time averaging is just to remove fluctuations in the state, not avoid the measurement problem. They're looking at time averages of the density matrix, which still yields a quantum object that will collapse upon measurement. And as their mathematical model points out, this can be true for arbitrary time averaging windows, the limits just change respectively as smaller time averages allow for larger fluctuations. There's nothing being swept under the rug here.
Simulations require supercomputers for doing large scale, detailed calculations, but simple situations can be solved completely analytically. For example, gravitational time dilation can be calculated somewhat simply for a central gravitational potential: https://en.wikipedia.org/wiki/Gravitational_time_dilation#Ou...
General Relativity is incredibly math heavy but fundamentally the numerical methods involved are standard methods for differential equations. The hard part is going from the math to a solvable form. See https://arxiv.org/pdf/2008.12931 for a broad overview. This will of course probably not make sense without an introduction to differential geometry, a beast of a topic itself. See some big textbook like https://arxiv.org/pdf/2412.08026 or find yourself a copy of Gravitation by Misner, Thorne and Wheeler.
This feels like lazy reporting. One beam isn't blocking the other, it's inducing a localized nonlinear process in a material which then absorbs the crossing beam. This isn't a novel process.
It's like me saying if I close a door I'm casting a shadow, sure, I caused it, but it's not my shadow.