And regarding the second part? In places where there is overlap between Judaism and the empirical world, like the effectiveness of prayers or giving the sota the bitter waters to drink, is there room to relate to empirical tests as indicators for proving the faith?

Definitely yes, except that such cases are very few, if any. One must also be careful not to be taken captive by interpretations or dogmas established by people.

“And it shall come to pass, if you surely listen…” And the verses following that, while the Sages interpreted that there is no reward in this world. Or in the world to come, “tomorrow to receive their reward,” etc.
That is the strongest empirical difficulty one can find.

Do you know how to interpret them? An interpretation that keeps Occam’s razor in its sheath.

I didn’t understand. What here requires interpretation? Occam’s razor is not relevant here. As I’ve explained more than once, the razor principle is always used under some set of assumptions. Someone who uses it as an exclusive principle will fall into many errors. You can search for this here on the site.

Hello Rabbi,
Many times people ask you the following question, but I haven’t come across a real, systematic response to it.
Seemingly, the religious claim is not a scientific claim—because it does not make falsifiable claims (Karl Popper).
But there are a few isolated cases where religion gives predictions that can be tested. And in those cases, it seems the predictions do not come true.
If so:

Would you expect to give extra weight to difficulties that arise from there, or not?
If not, how do you manage to reconcile these things—when many times that is not the plain meaning?
What would happen if you did not see any way to reconcile the difficulty—would you regard it as a refutation? And what would your conclusion about religion be?

Examples are numerous and scattered throughout the Torah, such as “so that it may go well with you,” “and you will prolong your days,” “and it shall come to pass, if you surely listen…,” “so that your days may be lengthened,” and so on.
And likewise from the Prophets, Jewish law, and aggadic literature, such as tithes, etc.

I don’t understand what “extra weight” means. Obviously, if there is a statement of the Torah that is not true, that is a problem. But the gates of interpretation have not been locked.
As I wrote above, I don’t think the examples are many. And even in those you cited, I don’t know how you know that this did not occur in the past. As for these later generations, I’ve written several times that over the generations divine involvement in the world has been diminishing. And regarding some of these, the Sages already expounded them as referring to “the day that is wholly long,” etc.

I don’t think you’re right. Even if the examples are not many quantitatively, they are not few in substance. It seems clear that there prevailed a conception of effects in this world through observance of the commandments.

Also, as I understand it, you are aware that what you’re saying is not really an interpretation of the texts; it doesn’t emerge from the texts, and it has no basis in the Torah’s text.
It follows from the fact that you think the involvement does not exist—so you force the answer that once it happened, but nowadays it no longer does, for reasons unknown to us.

But we don’t know what divine involvement in the world was like in the past; we don’t have much positive information on the matter, so this is just brushing off the difficulty.

Do you really not see any flaw in this??? To assume countless miracles and breaks in the laws of nature without explicit documentation of them? Did everyone who sent away the mother bird in those times live to 120? We would expect to see at least some mention of that.

—
How, as a scientist, are you not stirred by the possibility of proving empirically whether religion is true or not through predicting consequences for the future? These verses are our only possibility of verifying things. From here one should draw conclusions about the religious theory—whether to abandon it or revise it. What good are philosophical arguments if you’re blind to empirical attempts?

The claim that everyone who sends away the mother bird will live to 120 is a childish interpretation. Sending away the mother bird contributes to longevity, but there are many other factors as well. See my article on forced interpretations. Even if I very much wanted to put everything to an empirical test, there is no way to test this empirically, and therefore that is not an option. Now decide what you do with that.
That’s it. I’ve exhausted the topic.

Of course that is childish, and the words of the Hazon Ish about Havdalah are well known, but in any case one should have seen statistical significance, and still a verse does not depart from its plain meaning.

So I’ll ask: assuming we knew from an external source of knowledge that these verses have never been fulfilled, at any time (not even statistically), would that in your view negate the Torah’s credibility?

The claim that this cannot be tested empirically is completely incorrect. The verses are standing there and saying, “Test Me now with this,” and now the question is what you do with them.