You are correct about the replication problems, but this also varies heavily depending what scientific discipline you look at.

Also if you do science you may take the results oft another scientist (if they make sense and are peer revievewed) and build your next experiment on it, which may also work out and get peer reviewed.

So even with the replication problem science can work and build on thousands of experiments. But it would be better and needed that the experiments were reproducible.

I feel like there is a misunderstanding in this thread.

The universe is described by math. Math itself is also very fundamental though.

However even the Singularities are disputed and generally not liked by physicist. We try to find other explanations for how black holes work (lots of papers on this). Moreover, we never really have a singularity, but ringularities, as all black holes rotate changing the singularity to a singularity (they probably also have a charge but that is a different matter).

And on the other hand, if you are a follower of the simulation argument (I know a few physicists that are) there are also counter arguments against this (which I believe are more likely).

https://en.m.wikipedia.org/wiki/Simulation_hypothesis

I think you explain it pretty well, but one thing to add. Due to the General Relativity and thus spacetime it is actually not directions that all point toward the singularity, but as soon as you cross the event horizon all of your future becomes the Singularity, not as a point in space, but a point in time

https://plato.stanford.edu/entries/spacetime-singularities/lightcone.html

This points at that, you would also need to be able to travel faster than light and that would make you time travel backwards in time

You OK?

I am German, but I feel foremost European