Gemara

21b (R. Zeira): The oils and wicks forbidden to use on Shabbos may be used for Ner Chanukah on Shabbos or during the week.

(R. Yirmeyah): He forbids using the light.

(Rav Yehudah): One may not count coins near (using) the light of Ner Chanukah.

Objection (Shmuel): Does Ner Chanukah have Kedushah (that it is forbidden to benefit from it)?!

Objection (to the objection - Rav Yosef): Blood does not have Kedushah (yet the Mitzvah to cover it must be done honorably)!

(Beraisa): "V'Shafach... v'Chisahu" - he must cover with the same limb he used to slaughter, i.e. his hand.

He may not cover with his foot, lest Mitzvos be disgraceful in his eyes.

Here also, one may not count coins near the Ner, lest Mitzvos be disgraceful in his eyes!

Question: May one use Noyei (decorations of a) Sukah during Sukos?

Answer (Rav Yosef): We learn all Mitzvos (that one may not disgrace them) from covering blood.

23b (Rava): If one does not have enough money for Ner Shabbos and Ner Chanukah, Ner Shabbos has precedence, so there will be Shalom Bayis.

Rishonim

Rif (9a): R. Zeira permits to light Ner Chanukah, even on Shabbos, with oils and wicks forbidden for Neros Shabbos. He forbids using the light, therefore we are not concerned lest one tilt the Ner.

Ran (DH Hilchos): Ner Chanukah may not be used for anything, even for a Mitzvah. Since it commemorates a miracle with the Menorah, which may not be used, it was enacted to be similar to it. If it were permitted to use it for a Mitzvah, we would be concerned for tilting the Ner! Rav Yehudah teaches that even a petty use like counting coins is forbidden. He does not mean that we forbid only matters of Reshus (not a Mitzvah). The Yerushalmi says so, and the Rambam connotes like this, unlike Ba'al ha'Ma'or.

Rif (9b): One may not count coins near Ner Chanukah.

Ran (DH Amar Rava): It seems that Rava agrees that one may not use Ner Chanukah. If so, obviously one needs another Ner! He teaches that even though at a time of danger one leaves it on his table, and he is forced to benefit from it, still he needs another Ner for a sign (that the Ner is for the Mitzvah).

Rambam (Hilchos Chanukah 4:6): One may not use Ner Chanukah on Shabbos or on a weekday, even to use the light to check coins or count them.

Rosh (2:6): Above we ruled that Ner Chanukah may not be used for anything. Why did Rav Yehudah need to forbid counting coins? One might have thought that we forbid only major uses, for an onlooker will think that it was lit for this, but not for minor Arai uses. Rav Yehudah teaches that even a Arai task of Ganai (dishonorable) like counting coins is forbidden, for his hands are near the Ner to see well. This is why it says 'in front of Ner Chanukah', and not 'in its light.'

Mahari Segel (citing Re'em, brought in Maharal Minhagim, Sukos 9): We may not roast apples with Aravos used in Tefilah or for the Mitzvah. We save them to heat the oven to bake Matzos. Since they were used for one Mitzvah, we use them for another. Even though one may discard them, he may not step on them.

Poskim

Shulchan Aruch (OC 673:1): One may not use Ner Chanukah on Shabbos or on a weekday, even to use the light to check coins or count them, and even for uses of Kedushah, e.g. to use the light to learn.

Beis Yosef (DH Kasav): The Rosh connotes that a Arai use that is not Ganai, i.e. his hands need not be near the Neros, is permitted. Why didn't the Tur and R. Yerucham say so?

Taz (3): Why does the Beis Yosef permit only an Arai use that is not Ganai? Even if it is Ganai, like showing coins, if his hands need not be near the Ner, is permitted. He should not have mentioned Ganai regarding the usage, rather, Ganai to the Ner when his hands are close to it. The Maharshal says so. He forbids Arai uses such as showing coins, in which his hands must be close to the Ner, but permits other Arai uses. What forced the Rosh to mention Ganai? He just came to answer why Rav Yehudah needed to forbid counting coins, since Ner Chanukah may not be used for anything. It sufficed to answer that he forbids even Arai uses! Also, what is the Ganai? I say that our text of the Rosh is missing a word. It should say 'even Arai uses that are not Ganai, such as showing coins. Even without Ganai, this disgraces the Mitzvah. We forbid benefit from Noy Sukah due to disgrace to the Mitzvah. We forbid lighting a chip from a Ner Chanukah to light another Ner Chanukah due to disgrace to the Mitzvah. One opinion forbids even directly lighting one Ner Chanukah from another! Also Kitzur Piskei ha'Rosh did not mention Ganai. The Tur did not say opposite Ner Chanukah, rather, 'using the light.' This implies even if his hands are not near the Ner, like the Rosh inferred from Rav Yehudah's words [has he said 'using the light', we would forbid even far away] and like the Shulchan Aruch connotes.

Magen Avraham (2): The Beis Yosef, Darchei Moshe and Maharshal permit Arai uses when his hands are not near the Ner. The Bach is stringent. Semak and Sefer ha'Terumah forbid even eating near it. Also 678:1 connotes like this. (Ner Beiso has precedence over Ner Chanukah.) If one may use Ner Chanukah for Kedushah, he should light one Ner in his house, and he will have Shalom Bayis! Rather, all use is forbidden. This is the custom.

Gra (DH v'Afilu): (One may light Ner Chanukah on Shabbos with oils forbidden for Ner Shabbos. Since one may not use them, he will not adjust them.) If Kodesh use were permitted, this reason goes away. Also, Ner Beiso has precedence over Ner Chanukah. If one may use Ner Chanukah for Kedushah, he should light one Ner for both, and put it on his table, like it says in times of danger!

Rebuttal (Damesek Eliezer): We can say that if he buys oil and wicks forbidden for Ner Shabbos, it will last as long as needed for Ner Chanukah (until people cease from the market). If he buys oil and wicks permitted for Ner Shabbos, it will not last this long (but it will suffice for Shalom Bayis). In such a case, he cannot fulfill both. Rava teaches that he should fulfill Ner Shabbos. If he would use forbidden oils, he could not use the light, lest he tilt the Ner. Also, the light flickers and weakens, and he will need to go away. Perush ha'Mishnayos says that this is why the Pasul oils are forbidden.

Note: Perhaps the Gra's proof is built on what the Gemara said, that all oils are Kosher for Ner Chanukah on Shabbos, since he may not use the light. What is needed for Shalom Bayis is a Mitzvah, so if it were permitted, one Ner could fulfill both!

Mishnah Berurah (8): One may not benefit, so it will be recognized that the Ner is to publicize the miracle. Also, the miracle was done for the Menorah, which we do not use (its light) at all.

Mishnah Berurah (9): One may not even eat a Seudas Mitzvah through the light.

Mishnah Berurah (10): The Magen Avraham and Taz forbid even counting coins far from the Ner.

Kaf ha'Chayim (30): One may walk in the house by their light so he does not trip. This is not called usage.

Mishnah Berurah (13): Similarly, one may not use Neros [Chanukah] of the Beis ha'Keneses even for Kodesh uses, e.g. to pray Ma'ariv through the light, until they burned a half hour.

Shulchan Aruch (ibid.): Some permit uses of Kedushah.

Beis Yosef (DH u'Mah she'Chasav): Ba'al ha'Itur forbids only Chulin uses, but permits Kodesh uses. Shibolei ha'Leket permits reading a Sefer through the light. This is not Ganai of the Mitzvah. It is honor! The Rosh disagreed.

Gra (DH v'Yesh): This opinion permits only Arai use. It seems that the Tur connotes like this. Even though he said that the Rosh disagrees, and the Rosh permits Arai uses, the Taz changed the text of the Rosh. Rather, it seems that he permits, since we learn from coins, which is Chol.

Damesek Eliezer: The Taz says that the Ba'al ha'Itur permitted only Arai Kodesh uses. It is still recognized that the Ner is for Chanukah. All know that it was not lit for Arai uses. Regarding Arai uses, we do not decree lest he tilt it. The Gra says that the Tur connotes like this. He says 'Kodesh uses are forbidden, such as learning, and other uses, even Arai uses like looking at coins. Ba'al ha'Itur permits Kodesh uses. The Rosh disagreed.' This connotes that Ba'al ha'Itur distinguishes between Kodesh and Chol regarding the last matter the Tur mentioned, i.e. Arai uses. However, the Tur said that the Rosh disagreed, and the Rosh permits Arai uses that are not Ganai! Therefore, we must say that Ba'al ha'Itur permits even Keva. However, the Taz changed the text of the Rosh to forbid Arai uses even without Ganai. The Gra says that our text of the Rosh is better. Why did Rav Yehudah need to specify showing coins? He should have mentioned learning Arai! Rather, only Arai uses of Ganai are forbidden, but not Arai uses of Kodesh. If so, Ba'al ha'Itur must permit Keva uses of Kodesh. The Rosh disagreed.

Kaf ha'Chayim (32): The first opinion in the Shulchan Aruch is primary. In pressed circumstances one may rely on the latter opinion.

Bi'ur Halachah (DH v'Yesh): The Taz says that even this opinion forbids Keva Kodesh uses. If so, perhaps the first opinion permits learning Arai. Perhaps the Magen Avraham forbids only eating Keva through their light. Surely eating on Shabbos is Keva! Eliyahu Rabah and Chemed Moshe permit. The Rosh permits Arai uses. Even if we rule like the Magen Avraham, who forbids Arai uses even when his hands are not near the Ner, unlike the Beis Yosef, Darchei Moshe and Maharshal, perhaps all permit a Kodesh Arai use. This requires investigation. Perhaps even learning Keva is forbidden only in the Shi'ur (the half-hour that the Neros must burn). Even if one is stringent after this, unlike the Mechaber, he need not be stringent about Mitzvos. On a weekday if he has no other Ner, it is better to extinguish it after the Shi'ur and relight it.

Shulchan Aruch (OC 21:1): If Tzitzis strings snapped one may throw them in the trash because it is a Mitzvah without intrinsic Kedushah. However, as long as the strings are attached one may not use them, e.g. to tie something, for this disgraces the Mitzvah.

Tur: The She'altos (Korach 126) forbids a Yisrael to do his needs with something used to fulfill a Mitzvah, e.g. to tie something with Tzitzis strings, to smell Hadasim or to eat an Esrog. We learn from Kisuy ha'Dam. Tashmishei Mitzvah may be thrown away only after the Mitzvah has passed.

Rebuttal (Tur): We learn from Kisuy ha'Dam that Mitzvos may not be done disgracefully. However, if a Mitzvah was done honorably, it is not disgraceful to benefit from it afterwards. Tzitzis have no Kedushah; they are Tashmishei Mitzvah. One may throw them out or enter a Beis ha'Kisei with them. It seems to me that this is even when the Mitzvah applies; it is good to be stringent.

(Taz 1): The She'altos and Tur argue about benefit from Tzitzis while wearing the garment. The Tur holds like Tosfos (Shabbos 22a DH Sukah), who requires two reasons to forbid Noyei Sukah (decorations) even on Chol ha'Mo'ed and even if they fell. Firstly, they are Muktzeh at the beginning of Sukos (Yom Tov). Secondly, they are Muktzeh to the Mitzvah. The first reason does not apply to Tzitzis. All cases of benefit the Gemara forbids are either when both reasons apply, such as benefit from the four Minim, or when one wants to simultaneously do the Mitzvah and benefit from it, e.g. during the time Ner Chanukah must burn. This disgraces the Mitzvah itself. Regarding Tzitzis one can decide not to consider them to be a Mitzvah while using them. One cannot do so for Ner Chanukah, for its Mitzvah is to light it to burn continuously for the Shi'ur.