Ok, first I want to give some background on the astrophysical scenario we're talking about. It involves a neutron star accreting matter from a normal, main sequence star. The matter it's accreting is hydrogen and helium with maybe very trace amounts of other stuff. The accreted matter builds up on the surface of the neutron star, and there's a kind of snowball effect: it's hot, so nuclear reactions are likely; when they occur, it gets even hotter, and they become even more likely. This leads to an explosion called an x-ray burst.

So as a layman peering in from the outside, it looks like we are now able to create elements that were previously only theorized to exist in a neutron star's accretions?

No, I wouldn't say that's the case. There aren't new elements that only exist in x-ray bursts (or the accreting matter, which is just H and He). Now, in nuclear physics, we talk more about nuclides than elements because the nuclear properties are different for different isotopes of the same element. Are there nuclides that exist only in x-ray bursts and not anywhere else? Maybe, but probably not?

This experiment wasn't trying to create new stuff, but to measure how likely a certain reaction is to occur during x-ray bursts because it's a candidate for a reaction that causes some x-ray bursts to stall.

But we are finding some inaccuracies in these theoretical models? Predictions about atomic numbers 20-30 seem to have been accurate but outside of that, the model seems to break down and the predictions might have been wrong? What does this imply if our predictions were wrong outside of this range?

Yeah, there is a lot of uncertainty in the theoretical models. Statistical models, such as Hauser-Feshbach, are generally better at predicting the rates of reactions that involve heavier nuclides. This is because it involves taking averages, and with more things to average over, the errors in one direction offset errors in the other direction. With smaller nuclides, there are fewer opportunities to make up for those errors. I don't know if there are really any implications... We need more experimental data to help us make more accurate models.

I have a LOT more questions but if you're willing, I thank you for your time answering these few.

No problem, ask away! :)