1) LOOKING FOR ANSWERS
QUESTION: The Gemara cites the opinion of Rebbi Yitzchak who maintains that one may move a utensil on Shabbos only for the sake of something which is not Muktzah. The Gemara challenges his opinion from all of the cases cited by the Gemara earlier. The Gemara answers that none of those cases pose a difficulty to Rebbi Yitzchak, because they all refer to a person who picked up a utensil for a permissible use (in which case one may put the utensil down wherever he wants, even to cover a Muktzah item).
This answer resolves all of the questions. Why, though, does the Gemara continue to ask new questions if it knows this answer?
ANSWER: TOSFOS (DH Kofeh) says that although the Gemara knows this answer, it asks additional questions because it is looking for other answers.

43b----------------------------------------43b

2) COVERING A "MES" ON SHABBOS
QUESTION: Rebbi Yitzchak maintains that one may not move an item on Shabbos for the sake of something which is Muktzah. The Gemara asks how, according to Rebbi Yitzchak, one may bring a covering to cover a corpse (to protect it) which is Muktzah. Rav Huna explains that the permissible procedure is as follows: two people should sit down next to the body, and when they begin to get hot from the ground beneath them, they should go and bring couches upon which to sit. When they get hot from being unsheltered, they should go and bring a mat to hold above their heads. Then, while holding the mats above their heads (and above the body), they should lift the couches to support the mat, and then they may depart, leaving the body properly sheltered.
Why must the two people first bring the couches and then bring the mat? They should simply bring both the beds and the mat at the same time!
ANSWERS:
(a) TOSFOS (DH Cham) explains that the real purpose of the mat is to cover the body. However, to do so outright with the mat is prohibited, because one may not move an item for the sake of something that is Muktzah (according to Rebbi Yitzchak). In order to permit covering the corpse with the mat, the shelter must be erected for the sake of a living person and not for the corpse. Accordingly, the Rabanan required that one show that the mat is for his personal benefit. When he first brings the couch to sit on, he thereby does an action for himself first, and thus when he brings the mat it is not obvious that the mat is for the sake of the body.
(b) The RAMBAM (Hilchos Shabbos 26:22) writes that they do not use the couches to make the shelter. Rather, they merely leave two mats leaning against each other (like a teepee) above the body. Why, then, do they bring the couches? The KESEF MISHNEH explains that since their true intention when bringing the mats is not to protect themselves from the heat, but rather to shelter the corpse, they must make it look like they are bringing the mats for their personal use. Bringing the couches, which remain for their own personal use and are not used for the corpse, gives the appearance as if the mats are also brought for their personal use.
3) HALACHAH: THE PROCEDURE FOR COVERING A "MES" ON SHABBOS
OPINIONS: The Gemara discusses at length the procedure for covering the body of a dead person on Shabbos. What is the Halachah?
(a) The RIF and ROSH omit the entire discussion of the Gemara concerning how to cover a body on Shabbos. It seems that they omit it because the Gemara's discussion is only according to the view of Rebbi Yitzchak, who prohibits moving any object for the sake of an object that is Muktzah. Since the Halachah does not follow Rebbi Yitzchak, one is permitted to carry an object to the body, with no pretenses, in order to cover it.
(b) The RAMBAM and TUR record the Gemara's conclusion that a covering for the corpse may be brought only under the pretenses of using it for living people (see previous Insight). The BEIS YOSEF (OC 311) explains that the reason a body must be covered in this manner is not because it is prohibited to carry a mat for an object that is Muktzah. Rather, it is because erecting a mat as a shelter constitutes the Isur d'Rabanan of building a temporary tent. (Even a shelter that is pointed at the top and does not have a ceiling with a width of one Tefach may be made only for a live person, but not for a dead person.)
What is the Rambam's source that Rav Huna is discussing the prohibition of building a temporary tent? It seems clear from the Gemara that Rav Huna is explaining how to circumvent the prohibition against moving an object for something that is Muktzah, and not how to circumvent the problem of building a tent!
TOSFOS and the RIF point out that Rav Huna elsewhere (154b) seems to argue with Rebbi Yitzchak. Accordingly, the real reason why Rav Huna requires that the shelter for the Mes be made in this manner must be because of the problem of making a tent (and not because of the problem of carrying an object for the sake of placing it over a Muktzah object).
(However, we may ask another question on the Rambam's explanation. If one is permitted to carry an object for the sake of a Muktzah object, why must one perform this complex procedure in order to cover the corpse? One should just spread a mat directly over the corpse, with no space between the mat and the corpse (such that no Ohel is formed). The answer must be that one usually wants air to circulate around the body, and the only way to achieve this is to leave a tent above the body, as the Rambam describes. -M. KORNFELD)

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