Mr. Braun received legal notice: Mr. Rubin was demanding $50,000 payment due.

“I owe no more than $10,000,” replied Mr. Braun. “I’m willing to pay that amount immediately to settle the issue.”

“Our records indicate $50,000,” came the response. “If the full amount is not paid, we will proceed to take legal action in court.”

“I deny owing that amount,” replied Mr. Braun. “If there is need for litigation, though, I request that we adjudicate in a Jewish beis din.”

“We refuse to mediate in beis din,” Mr. Rubin’s lawyer responded. “In light of your denial, we are filing a suit in civil court.”

Mr. Braun received a summons to a court hearing. After some deliberation, the judge dismissed the case and exempted Mr. Braun completely.

Mr. Braun walked out feeling great. Not only was Mr. Rubin’s claim rejected, but he was exempted even from the $10,000 that he actually owed.

A short time later, Mr. Rubin filed a claim in beis din. Mr. Braun alerted the dayanim that he had initially wanted to adjudicate in beis din, but Mr. Rubin refused. “The case was already heard in civil court, and dismissed,” he said. “I’m not interested in adjudicating again.”

When beis din heard this, they decided not to accept the case. “We generally don’t accept cases that have already been adjudicated in civil court, unless both sides want to re-adjudicate.”

“So I’m off scot free?” asked Mr. Braun. “Am I obligated to pay the amount that I know I owe?”

“According to many authorities, yes,” replied Rabbi Dayan, “even though beis din refrains from accepting the case, but some exempt.”

“Could you please explain?” he asked.

“Rema (C.M. 26:1) sides with the opinion that beis din should refrain from adjudicating a case that the plaintiff previously brought to civil court and lost,” explained Rabbi Dayan. “Rav Yonasan Eibeschutz, in Tumim (26:2), questions this ruling: Even if the civil court ruled against the plaintiff, what exempts the defendant from his obligation according to Torah law?”

“Tumim provides two explanations,” continued Rabbi Dayan. “One, the Rema follows his own ruling (C.M. 22:2) that although a Jew is not allowed to accept the authority of a non-Jewish judge, after adjudicating before him the person cannot retract, as he implicitly accepted the judge as qualified. However, the Shach (22:15) questions this ruling and further requires a formal kinyan sudar of this acceptance.”

“What is the second explanation?” asked Mr. Braun.

“Since the plaintiff violated Halachah by adjudicating in civil court, as a penalty to him beis din declines to look after his interests,” replied Rabbi Dayan. “The Gra (26:4) indicates this reason, as well.”

“Is there a practical difference between these two reasons?” asked Mr. Braun.

“In a case where the defendant bribed the non-Jewish judges in his favor, that ruling is null and void, so that the first reason would not apply,” replied Rabbi Dayan. “Nonetheless, the Nesivos (26:2) suggests that a second reason of penalty, which he considers primary, still applies, so that beis din should decline the case, regardless.”

“What about my question?” asked Mr. Braun.

“Nesivos and Aruch Hashulchan (26:1) write that although beis din avoids adjudicating the case, the defendant remains obligated to pay what he owes,” replied Rabbi Dayan. “Even if he is unsure, he should consult the beis din to avoid potential theft.”

“However, according to Tashbetz (3:86), since the parties went to adjudicate before the civil court, it is as though they accepted upon themselves to judge in that manner and forwent their rights according to Torah law,” concluded Rabbi Dayan.

“Tumim also implies that, since you are holding the money, you can rely on the Rema’s ruling (22:2) that the non-Jew’s decision is valid post facto and would not have to pay.” (See also Maharsham 1:89; Minchas Pittim, C.M. 26.)

I left my umbrella in shul. About a week later I found an umbrella that looks like mine in the coat room where I had left my umbrella.
Q: May I assume that the umbrella I found is mine and take it?
A: Many times it happens that someone loses something and then finds an item that looks similar to the one he lost but cannot honestly state that it is his own. Two discussions in the Gemara have a bearing on this question.
The Gemara (Pesachim 10a) discusses a mouse with bread in its mouth that runs into a room that had already been checked for chametz. The owner follows the mouse and discovers some bread. May he assume that the bread he found is the same bread that the mouse brought into the room, or is he required to search the entire room again for chametz? Poskim debate whether one may assume that the found bread is the same bread the mouse brought in. Some contend that if the owner already nullified his chametz the potential violation would be Rabbinic, and one may assume that he found the mouse’s bread. 
Others contend that even if one did not nullify his chametz so that the potential prohibition is Biblical, one may assume that he found the mouse’s bread (O.C. 439:2; Noda BiYehudah 1, E.H. 46).
On the other hand, the Gemara (Gittin 27a) addresses a delivery agent who lost a get. The Gemara rules that if he finds it immediately, the get remains valid without concern that the get he found belongs to another couple. If he did not find the get immediately and cannot be certain that the found get is the one he lost, he may not deliver it to the intended woman, because we are concerned with the possibility that it is not the get that he lost. Clearly, this Gemara indicates that for Biblical matters we are concerned that one did not find the object that the agent lost (E.H. 132:4). Poskim discuss the difference between the two gemaros; those distinctions have bearing on your case.
Some authorities note that these discussions are not applicable to your case. Although an object’s location is a siman (identifying feature), nevertheless, when someone claims to be the owner by identifying its location, we rule that knowing the location is not a siman since others also place similar objects there (C.M. 262:9). Therefore, stating that your umbrella was lost in a shul coatroom does not prove that you are its owner (Minchas Yitzchak 3:17).
There is, however, a rationale that permits you to take the umbrella. The umbrella does not have a siman. Consequently, if the owner already realized that his was lost you may certainly take it, since he despaired (yei’ush) of recovering it. Moreover, even if it is possible that the owner does not yet realize its loss (yei’ush shelo midaas) — and generally in such a circumstance one may not take the lost object — in this instance it is permitted. That restriction is limited to objects that one knows is not his. Therefore, if the owner proves the object is his, it must be returned.
In your case, since it is possible that the umbrella is yours, and since it does not have a siman, it will be impossible for anyone else to prove that he is the true owner, so no one would be able to take it from you. Furthermore, there is no concern for a hidden siman because if that was a concern, one would never be able to keep a lost object. Thus it is permitted for you to take the umbrella (Pischei Choshen, Aveidah 3:18).

Q: I rented a room at a certain price per month, without a specified time limit. Can the landlord raise the rent after three months?
A: When the rental agreement specifies a time frame, neither side can retract or unilaterally change the rent during the specified time, even if there is a significant, unexpected change in rental rates (C.M. 312:1, 10; 316:1).
If the rental agreement simply states the fee per day, month, week or year, without specifying a time, the price continues so long as the renter remains. However, either side can retract or demand to adjust the rental fee in order to continue the rental. (Real-estate rental often has a 30-day or one-year minimum, in accordance with local practice — C.M. 312:9; 341:1; Aruch Hashulchan 312:12.)
If there was a specified time frame and the renter continued residence without explicitly renewing the contract, there is a dispute whether the owner can retroactively charge the current, higher rate without having notified the renter beforehand (see Shach 312:10; Machaneh Ephraim, Sechirus #11).