A. First of all, the points are illuminating and insightful, but the very claim that because the religious court has no reason to rule, therefore the law of the money remains in its current state, seems to me very strange. Why should the court’s ruling affect monetary ownership? Beyond that, afterward you wrote that where the possessor knows that he is justified in his possession, he may use the object. My question is: why not explain the rule that the burden of proof is on the claimant this way — namely, that my very knowledge that I am in the right (or even knowledge that the doubtful side favors me) gives me the right to continue holding it and to exercise that right. In that sense the claimant is like “the one who has pain,” in that he is the one obligated to go to the doctor and take care of himself, and there is no demand on the healthy person to help him. That is, the state of the possessor and the claimant is like the state of the sick person and the healthy one.
B. You also didn’t explain there the presumption that whatever is in a person’s possession belongs to him, which is certainly an assumption about reality, since there “somewhere else” forceful seizure would not help at all, even according to Maimonides, and this is explicit in several places. So it must be that where there is no monetary tie, there is some sort of presumption that the possessor is in the right (I have no idea why one should assume that; on that I agree with you), and therefore forceful seizure is ineffective.
Thanks, and blessings for your strength

The court’s ruling does not affect ownership, but only the court’s own actions. If it has no reason to intervene, it does not intervene.
I didn’t understand the second question. Even if he has the right to use it, the court is not obligated to take that into account. Nor is there any necessity that the possessor is actually telling the truth and knows what he is saying. It is possible that he is lying.
I explained why that presumption is not a correct factual assumption. So what is the question? There is reason to establish such a presumption in Jewish law, and therefore it has the status of a presumption.

A. If it does not affect ownership, then what good would betrothing a woman with this money do? If so, we have emptied the rule that the burden of proof is on the claimant of all content, and it is merely a technical instruction to the court.
B. I would say that the very fact that the court knows that he knows it is his — that itself should cause them to rule that the possessor has a full right to keep it by virtue of his knowledge. In my humble opinion, the court has no right to assume that one of them is lying, and the simple assumption is that one of them is mistaken.
C. “There is reason to establish such a presumption in Jewish law” — meaning, we will make assumptions about reality just so we can have fun? Really?

A. I didn’t understand the question. If that person thinks the money is his, he takes it and betroths a woman with it, and she is indeed betrothed. But not because the court allowed him to do so, rather because the money really is his.
C. Not for fun, but because there are legal reasons to assume it.