1) THE "CHUMROS" OF TERUMAH AND BIKURIM OVER MA'ASER
QUESTION: The Gemara quotes the Mishnah in Bikurim (2:1-2) which contrasts the laws of Terumah and Bikurim with the laws of Ma'aser Sheni and describes the ways in which Terumah and Bikurim are more stringent than Ma'aser, and the ways in which Ma'aser is more stringent than Terumah and Bikurim. Among the stringencies of Terumah and Bikurim are the laws that a Zar (non-Kohen) who willfully eats them is Chayav Misah, a Zar who accidentally eats them must pay an additional Chomesh (a fifth of their value), and a Zar is prohibited from eating them.
Since the Mishnah states that a Zar is Chayav Misah for willfully eating Terumah and Bikurim, and must pay a Chomesh for inadvertently eating them, it is obvious that he is prohibited from eating them! Why does the Mishnah mention as an additional stringency that Terumah and Bikurim are prohibited to a Zar? (TOSFOS, TOSFOS YESHANIM)
Moreover, the Gemara in Yoma (73b) asks why the Mishnah there states that eating and drinking are prohibited on Yom Kippur. Since the Mishnah there already states that one who eats and drinks on Yom Kippur is punished with Kares, it is inappropriate to mention that those acts are merely "prohibited." Similarly, why does the Mishnah in Bikurim mention that Terumah and Bikurim are "prohibited" to a Zar? A Zar is not merely prohibited from eating them -- he is even punished with Misah! (ME'IRI)
ANSWERS:
(a) RASHI in Bava Metzia (53a, DH va'Asurim) answers that the Mishnah mentions the words "Asurim l'Zarim" only because it wants to conclude with the words "Mah she'Ein Ken b'Ma'aser" and contrast the laws of Terumah and Bikurim with Ma'aser. By adding the words "Asurim l'Zarim," the Mishnah teaches that Ma'aser differs from Terumah and Bikurim not only in that a Zar is not punished for eating it, but in that a Zar is permitted to eat it even l'Chatchilah. "Asurim l'Zarim" teaches by inference that Ma'aser is permitted to Zarim.
TOSFOS (here and in Bava Metzia) rejects this explanation. He points out that the first part of this Mishnah, which lists the stringencies of Terumah and Bikurim, is recorded again in a Mishnah in Chalah (1:9), which lists the stringencies of Chalah and Bikurim. There, however, the Mishnah also begins by saying that Chalah and Bikurim are "Asurim l'Zarim," but it does not conclude by contrasting the laws of Chalah and Bikurim with the laws of Ma'aser! According to Rashi's explanation, the Mishnah in Chalah has no need to mention "Asurim l'Zarim."
The RITVA defends Rashi's explanation. He writes that occasionally a Mishnah uses the same wording it uses elsewhere even though that wording is not fully appropriate in the present context. (See, for example, Makos 2:8, "k'Yotzei Bo, Rotze'ach...," which is based on the wording of the Mishnah in Shevi'is 10:8.) The Mishnah in Chalah borrows the wording of the Mishnah in Bikurim even though the words "Asurim l'Zarim" are unnecessary in the Mishnah in Chalah.
(b) RASHI here in Yevamos apparently follows a different approach. When the Mishnah says that one is punished with Misah for intentionally eating Terumah and Bikurim, it does not refer to a Zar who eats Terumah and Bikurim but to a Kohen who is Tamei who eats Terumah and Bikurim. This also seems to be the intent of Rav in the Yerushalmi in Bikurim (2:1). (See MAHARSHA; see also RASHASH and ARUCH LA'NER who suggest another reason for why Rashi writes that the Mishnah discusses a Kohen who is Tamei, and not a Zar.)
Why, though, does the Mishnah mention that Terumah and Bikurim are "Asurim l'Zarim" if it already mentions that one must pay a Chomesh for eating them? A Kohen who is Tamei does not pay Chomesh for inadvertently eating Terumah or Bikurim! Perhaps Rashi maintains that the fact that one is obligated to pay a Chomesh for eating Terumah is not a definite indication that he is prohibited from eating it (as the Me'iri explicitly writes). One might have thought that he is permitted to eat Terumah but must pay a Chomesh if he does. Therefore, the Mishnah must add that one is prohibited to eat Terumah and Bikurim. (See, however, RASHI to Gitin 21b, DH Lo Efshar.)
(c) The ARUCH (Erech "Te'an") answers that "Asurim l'Zarim" teaches that Terumah and Bikurim remain prohibited to a Zar even after they are redeemed with Pidyon. In other words, the Mishnah teaches that Terumah and Bikurim cannot be redeemed with Pidyon, in contrast to Ma'aser which may be redeemed.
TOSFOS, however, rejects this answer because Rav Ashi (74a) states that the Mishnah omitted the stringency that Terumah and Bikurim cannot be redeemed, and that this was one of several stringencies which the Mishnah intentionally omitted ("Tana v'Shayar").
Perhaps the Aruch understands that the other Amora'im in the Gemara disagree with Rav Ashi and maintain that the stringency of "Ein Lahem Pidyon" was not omitted from the Mishnah but was included in the Mishnah in the words "Asurim l'Zarim." The Aruch intends only to explain the wording of the Mishnah according to those Amora'im.
(d) The ARUCH cites another answer in the name of Rebbi Yochanan in the Yerushalmi (Bikurim 2:1). The Yerushalmi suggests that "Asurim l'Zarim" refers to the prohibition against eating "Chatzi Shi'ur" (less than the minimum amount necessary for being punished). A Zar who eats a "Chatzi Shi'ur" of Terumah is neither punished with Misah nor required to pay Chomesh.
However, the Gemara in Yoma (73b) teaches that the prohibition of "Chatzi Shi'ur" applies to all prohibitions in the Torah. Accordingly, why does the Mishnah need to state this Halachah specifically with regard to Terumah and Bikurim?
The TOSFOS YESHANIM and other Rishonim answer that eating Terumah and eating Bikurim are prohibitions which are not "Shaveh ba'Kol" -- they do not apply to all Jews equally (since they do not apply to Kohanim). One might have thought that the Torah (or Rabanan; see Yoma 73b) does not prohibit a "Chatzi Shi'ur" of such prohibitions. Therefore, the Mishnah teaches that even a "Chatzi Shi'ur" of Terumah and Bikurim is prohibited.
(e) The ME'IRI (in the name of "Yesh Mefarshim") explains that "Asurim l'Zarim" means that Terumah and Bikurim are Asur b'Hana'ah -- one is prohibited to derive any form of benefit from them. Although there are forms of benefit which one may derive from Terumah, those forms of benefit are permitted only when the Terumah will not be consumed in the process. One may not derive benefit from Terumah in a manner which does not preserve the Terumah itself. (See TOSFOS to 66b, DH Lo.)
One who derives benefit by destroying Terumah is not punished with Misah or Chomesh, but he does transgress a prohibition. This is the intention of the Mishnah when it states that Terumah and Bikurim are "Asurim l'Zarim." (See MITZPEH EISAN for another answer.)

73b----------------------------------------73b

2) IN WHAT WAY IS "MISAH B'YEDEI SHAMAYIM" MORE SEVERE THAN "KARES"
QUESTION: The Gemara compares Terumah to Kodshim and attempts to prove that Kodshim is more severe ("Chamur") than Terumah. In one attempt, the Gemara points out that the punishment for one who is Tamei who eats Kodshim is Kares (early death and childlessness). The Gemara counters that perhaps Terumah is more "Chamur" because one who is Tamei who eats Terumah is punished with Misah b'Yedei Shamayim (death at the hands of heaven).
In what way does the punishment of Misah b'Yedei Shamayim indicate that Terumah is more "Chamur" than Kodshim? The punishment of Kares includes the death of one's children, but Misah affects only the transgressor himself. Moreover, one who is punished with Kares dies between the ages of 50 and 60, but one who is punished with Misah dies only before his destined time, but he can live to be older than 60. (See Background to the Daf.)
These differences make it clear that Kares is more severe than Misah. Why does the Gemara respond that Misah b'Yedei Shamayim is more severe than Kares?
ANSWERS:
(a) TOSFOS (DH she'Ken) answers that when the Gemara mentions Misah it does not refer to the punishment for one who eats Terumah while he is Tamei. Rather, it refers to the punishment for a Zar (a non-Kohen) who eats Terumah. The punishment for a Zar who eats Terumah is Misah b'Yedei Shamayim, while the punishment for a Zar who eats Kodshim is Malkus (see also Rambam, Hilchos Ma'aseh ha'Korbanos 11:8), and not Misah or Kares. In this respect, Terumah is more "Chamur" than Kodshim.
However, Rashi (DH Pigul and DH Machpaz) explains that the Gemara refers to a Kohen who is Tamei who eats Terumah and Kodshim, and not to a Zar who eats Terumah and Kodshim.
(b) TOSFOS RABEINU PERETZ (in Pesachim 32b) quotes RABEINU SHMUEL of Evreux who cites the Yerushalmi that states that Misah is more severe than Kares in one respect. When one is punished with Misah, all of his possessions are also destroyed. In contrast, when one is punished with Kares, his possessions are spared. This is also the opinion of RABEINU YONAH (Sha'arei Teshuvah 3:6:1): the punishment of Misah includes the eventual destruction of a person's animals and possessions, as the verse says, "Alah Maves b'Chaloneinu" (Yirmeyahu 9:20).
Perhaps this phenomenon -- that Misah is more severe than Kares in one respect -- may be understood as follows. The Gemara in Sanhedrin (48b) teaches that "when the court kills a person [who deserves the death penalty], his belongings pass to his legal heirs. However, when the king kills someone for disobeying his word, the king takes the person's property." Kares is a punishment meted out by the court -- the "heavenly court." The heavenly court administers Kares when the earthly courts are unable to prosecute the perpetrator (for example, the sinner did not receive proper Hasra'ah, warning, from witnesses before the act). In the framework of Torah punishments, Kares is in the same category as Misas Beis Din.
In contrast, Misah b'Yedei Shamayim is punishment "at the hands of heaven." It is carried out by the King, Hash-m Himself, when a person disobeys Him and slights His majesty in a particular way. Specifically, Misah b'Yedei Shamayim is administered to those who defile His chosen portion or sanctuary. (Examples of this are a non-Kohen who eats Terumah, Bikurim or Chalah, a Kohen Tamei who eats Terumah, one who eats Tevel from which Terumah was not separated, one who misuses Hekdesh (according to Rebbi), improper behavior in the Mikdash such as a Zar who performs the Avodah or a Kohen who enters the Kodesh ha'Kodashim for no reason; see RAMBAM, Hilchos Sanhedrin 19:2. It is interesting to note that even the instances of Misah b'Yedei Shamayim "d'Rabanan" that Rabeinu Yonah lists (ibid.) fit precisely into this category.)
When Misah is administered, the person is killed for having offended the King. Just as an earthly king, who executes a person who disobeyed him, takes away all of the person's property, so, too, Hash-m, the King, confiscates the guilty party's property and takes back what was always His. (M. Kornfeld; see also Insights to Pesachim 32:2.)