1) DERIVING PLEASURE IN UNUSUAL WAYS
QUESTION: The Gemara states that if one makes a Neder not to have pleasure from his friend's food, the Neder prohibits him from chewing his friend's wheat kernels and placing them on his wound in order to heal it.
This prohibition is difficult to understand. Most types of pleasure which the Torah prohibits (Isurei Hana'ah) are prohibited only when the pleasure is derived in a normal manner (k'Derech Hana'asan). (The Rabanan prohibited deriving pleasure from an Isur Hana'ah in an unusual manner as well.) The MAGEN AVRAHAM (OC 466) writes that the use of wheat kernels to heal one's wounds is not a normal form of deriving pleasure from wheat kernels. Why, then, does the Gemara assume that one who prohibits himself from deriving pleasure from wheat has intention to prohibit himself even from an unusual form of pleasure?
ANSWER: TOSFOS in Avodah Zarah (12b) writes that when Hana'ah is prohibited, even unusual forms of Hana'ah are prohibited. The rule that an unusual form of Hana'ah is permitted applies only when the Torah uses the phrase "do not eat" to express the prohibition against having pleasure from an item. In such instances, the Torah means that only normal forms of deriving pleasure, similar to the pleasure of eating, are prohibited. Accordingly, when one makes a Neder not to have "pleasure," even unusual pleasures are prohibited.
This answer is problematic. The Gemara in Pesachim (26a) teaches that one is permitted to sit in the shade of the walls of the Beis ha'Mikdash since its walls were made to serve the inside of the Beis ha'Mikdash and not for the purpose of making shade outside. RASHI and TOSFOS there explain that deriving benefit from the walls of the Beis ha'Mikdash in this manner is permitted because it is a benefit which is derived in an unusual manner (i.e. providing shade outside is not the purpose of the walls of a building). However, since Hekdesh is a form of Neder, why is one permitted to derive pleasure from an item of Hekdesh (the walls of the Beis ha'Mikdash) even in an unusual manner?
This question may be answered based on the words of Tosfos in Pesachim there. Tosfos asks why is one permitted to derive pleasure from Hekdesh in an unusual manner if the Torah does not use the phrase "do not eat" to teach the Isur of Hana'ah from Hekdesh. Tosfos answers that the Isur of Hana'ah from Hekdesh is derived through a Gezeirah Shavah from Terumah, where the Torah does use the phrase "do not eat." Therefore, deriving pleasure from Hekdesh, too, is permitted when it is not done in a normal manner.
This explains why one is permitted to derive pleasure from Hekdesh in an unusual manner (the Isur of Hana'ah of Hekdesh is prohibited by the Torah with the phrase "do not eat" via a Gezeirah Shavah). In contrast, when one makes a Neder and specifically states that pleasure is forbidden, all pleasures are included in his Neder, even those derived in an unusual manner.

33b----------------------------------------33b

2) PAYING A DEBT ON BEHALF OF A PERSON TO WHOM ONE IS PROHIBITED TO PROVIDE BENEFIT
QUESTION: The Mishnah (33a) states that when one makes a Neder not to give pleasure to his friend, he is permitted to pay the half-Shekel donation to the Beis ha'Mikdash on his friend's behalf, and he is permitted to pay his friend's debts for him. The Gemara explains that paying his friend's debts is permitted since his act is considered only as though he "chases away a lion" from attacking his friend or his friend's property (that is, he prevents damage from occurring, but he does not actively provide benefit).
Rav Hoshiya explains that the Mishnah expresses the opinion of Chanan who maintains that one who pays his friend's debts cannot force his friend to pay him back.
Although his friend is not required to pay him back, he still derives pleasure from the fact that he does not have to pay back his debts. Why is he permitted to receive this pleasure from the person from whom he is prohibited to have pleasure?
ANSWERS: The Rishonim provide two basic explanations for why one is not required to compensate the person who paid his debts.
(a) TOSFOS in Bava Kama (58a; see also Tosfos and Ritva here) explain that one is required to repay any monetary pleasure that he received. Even if that pleasure came merely because he was saved from potential damage, he still must pay since he saved money through his friend's act. Hence, he is not considered to have received benefit since he must reimburse the benefactor. The only case in which he is not required to pay back is a case in which he would not have lost his own money even if his friend would not have paid the debt for him, and by paying for him his friend merely saved him from discomfort but not from any actual monetary loss. Since a debtor is often able to convince his creditor to forgo the debt or find other friends or relatives to pay the debt for him, the one who pays the debt is not necessarily preventing the beneficiary from a loss and thus the beneficiary is not required to pay him back. Similarly, payment of his debts does not constitute a violation of the Neder that prohibits him from deriving benefit from his friend.
RABEINU TAM presents a similar logic, but he explains that Chanan agrees that when one pays his friend's debt for him, his friend must pay him back since he benefited by not having to pay back with his own money. Chanan's opinion applies only when one gives food (Mezonos) to his friend's wife and children (Kesuvos 107b) in his absence. In such a case, the benefactor is not considered to be saving the husband money, since the wife and children could have worked for their own food, in which case the husband would not have been obligated to buy them food (alternatively, they could have eaten less, as Tosfos in Kesuvos says).
These Rishonim seem to understand that "benefit" is defined as any benefit for which one must reimburse the benefactor; if one is not required to reimburse the benefactor, the act is not considered benefit. Alternatively, they understand that a Neder which prohibits one from receiving benefit includes only monetary benefit (benefit with a quantifiable value) from his friend. According to Chanan, paying one's debts is not a benefit that has a monetary value.
(b) TOSFOS in Kesuvos (108a, DH Ha Mani) understands that one whose debts have been paid by another has received benefit, but he is not required to reimburse the benefactor since the benefit was not given to him in a direct, positive manner, but rather in a passive, indirect manner (through the prevention of damage). Chanan maintains that this is considered an indirect form of giving pleasure ("Gerama") and does not require reimbursement.
Rav Hoshiya proves from Chanan's ruling that the benefit in this case is given only indirectly, and that is why the person whom the Neder prohibits from receiving benefit may receive this benefit (see Nedarim 43a).
3) PAYING THE HALF-SHEKEL ON BEHALF OF A PERSON TO WHOM ONE IS PROHIBITED TO PROVIDE BENEFIT
The Mishnah (33a) states that when one makes a Neder not to give pleasure to his friend, he is permitted to pay the half-Shekel donation to the Beis ha'Mikdash on his friend's behalf, and he is permitted to pay his friend's debts for him. The Gemara in Kesuvos (108a) explains that paying the half-Shekel for him is permitted because he is doing a Mitzvah.
TOSFOS in Bava Kama (58a, see previous Insight) and others explain that whenever one saves his friend from a definite loss of money, he has the right to be reimbursed. Why, then, is he permitted to pay his friend's half-Shekel obligation? Hekdesh cannot forgo the obligation, and therefore the benefactor is saving the beneficiary from a definite loss of money!
ANSWERS:
(a) The Gemara in Kesuvos (108a) answers that the Korbanos bought with the half-Shekel collection are bought on behalf of all of the people, even those who sent money which became lost on the way, and even those who did not yet send the money.
The RITVA here (and RASHI in Kesuvos) explains that since one has a share in the Korbanos even if he "never gives" his half-Shekel, the actual giving of the half-Shekel is only for the sake of the Mitzvah and is not for material gain. Hence, it is not considered a prohibited benefit to the person who is prohibited from receiving benefit because "Mitzvos Lav l'Hanos Nisnu" (Rosh Hashanah 28a) -- the physical benefit one derives from a Mitzvah is not considered benefit.
(b) TOSFOS here (33a) disagrees and maintains that one who never sends his half-Shekel does not have a share in the Korbanos. Tosfos explains that one is permitted to pay the half-Shekel for the person who is prohibited to receive benefit only when the beneficiary had already sent his own half-Shekel and it became lost on the way. In such a case, he already has a share in the Korbanos even if his lost half-Shekel is not replaced.
According to TOSFOS in Kesuvos, paying a debt is not considered direct benefit and therefore it is permitted even when the benefactor thereby saves his friend from a definite loss of money. Tosfos understands that the Gemara in Kesuvos means that even those who disagree with Chanan agree with the Mishnah here.
TOSFOS in Bava Kama (58a) also says that the Gemara in Kesuvos explains the Mishnah according to those who disagree with Chanan. According to Chanan, having one's debt paid is not considered benefit since he can either persuade the lender to forgo the debt or find other friends or relatives to pay his debts for him.