Due to the metric expansion of space, the universe is not time translation invariant at cosmological scales, hence no energy conservation via Noether's first theorem. However, Noether's second theorem still applies due to general covariance, and you get an 'improper' / 'strict' (terminology differs) conservation law for any time-like vector field (in case of cosmological time, this yields the first Friedmann equation). However, these laws are non-covariant as they include gravitational contributions that cannot be localized via a stress-energy tensor. It's somewhat similar to what happens to energy conservation in rotating frames of reference, except that there's no longer such a thing as inertial frames that make energy conservation manifest. Consequently, a large portion of physicists find it less confusing to just state that energy conservation doesn't hold for the universe at large.

> The tendency to expand due to the stretching of space is nonexistent, not merely negligible.

Note that this claim is at odds with one of the papers that is cited in support (ref. 19 specifically). The final sentence of arXiv:astro-ph/9803097 reads:

> As a conclusion, it is reasonable to assume that the expansion of the universe affects all scales, but the magnitude of the effect is essentially negligible for local systems, even at the scale of galactic clusters.

No. The solutions to the relativistic version of the Kepler problem are different from the Newtonian ones:

You still have hyperbolic-like, parabolic-like and elliptic-like solutions. However, the parabolic ones can loop around the black hole a couple of times before going off to infinity, and the elliptic ones will have their perihelion precess around it. Additionally, you get solutions that cross the horizon and never come back out, eventually hitting the singularity, and trajectories that asymptotically approach a circular orbit.

There is a 'theoretically': Tachyons would be able to cross event horizons.

Of course, we have no reason to believe that tachyons exist (and good reasons to believe why they don't), but if you're not careful, they may pop up in numerical simulations (that whole photon velocity being a null vector thing is a bit fragile if you do not take steps to enforce it algorithmically).