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Entering a Cemetery with Tzitzis: 
One may not enter a cemetery while wearing Tzitzis that are revealed to the open. This applies both to a Tallis Gadol and a Tallis Katan. If however the Tzitzis are covered and are not apparent at all to the outside, then it is permitted to enter the cemetery wearing it. [Thus prior to entering into a cemetery one is to tuck his Tzitzis into his pants, or pocket in a way that it will no longer be visible.]
Within four Amos of an open cemetery or grave: One who enters within four Amos [192 cm] of a grave or of a [open] cemetery is considered as if he entered inside the cemetery, and is thus required to cover his Tzitzis as explained above.
A closed cemetery: By a closed cemetery that has a wall or fence surrounding it, one should be stringent not enter into the cemetery while wearing [revealed] Tzitzis, even if he is a great distance from the actual graves. However outside the walls of the cemetery one may wear revealed Tzitzis even if he is within four cubits of a grave that is behind the wall.
A four cornered clothing: If one is wearing a four cornered garment with Tzitzis that serves as actual clothing to garb his body, and is not worn for the sake of the Mitzvah of Tzitzis, then one may enter with it into a cemetery even if the Tzitzis are revealed, so long as they do not drag on the ground. [In today’s times it is no longer common for people to wear four cornered garments with Tzitzis, other than a Tallis Gadol/Katan which is worn for the Mitzvah.]
Wearing Tzitzis near a corpse:
One may not wear revealed Tzitzis when he is near a corpse, just as is the law by a cemetery, and he is thus required to cover his Tzitzis as explained above. This applies for anyone that is within four Amos [192 cm] of a corpse.
One may not enter a cemetery while wearing Tzitzis that are revealed to the open. Thus, prior to entering into a cemetery one is to tuck his Tzitzis into his pants, or pocket in a way that it will no longer be visible. By a closed cemetery that has a wall or fence surrounding it, one should be stringent not enter into the cemetery while wearing [revealed] Tzitzis, even if he is a great distance from the actual graves. However outside the walls of the cemetery one may wear revealed Tzitzis even if he is within four cubits of a grave that is behind the wall.
May one wear a Tallis Gadol/Katan over his clothing in a cemetery if the actual Tzitzis are tucked in?
Some Poskim rule it is permitted to do so. Other Poskim rule it is forbidden to do so by a Tallis Gadol. Practically, one is to avoid wearing a revealed Tallis Gadol anywhere within the parameters of a cemetery, even if the Tzitzis are covered.
May one wear revealed Tzitzis in a gentile cemetery, or near a gentile grave?
May one wear revealed Tzitzis near the grave [or corpse] of a Jewish woman [that is not in a cemetery]?
May one wear revealed Tzitzis near the grave [or corpse] of a Jewish child [that is not in a cemetery]?
May one wear Tallis and Tefillin near the gravesite of a Tzaddik?
Tzitzis on a corpse:
The custom of all Jewry is to garb a [male] corpse in a Tallis Gadol at the time of his funeral and burial, as his form of Tachrichim. The custom is to wrap him in the Tallis Gadol that he wore while alive. Some are accustomed to invalidate one corner of Tzitzis prior to the burial, and so is the Chabad custom. Others however rule that the corpse is to be buried in Kosher Tzitzis. In Eretz Yisrael the custom is to bury the corpse without a Tallis, although he is garbed in a Tallis throughout the funeral, until the burial. In Eretz Yisrael, one may not swerve from this custom.
 Admur 23/1-2; Michaber 23/1; Brachos 18b regarding Tefillin and a Sefer Torah; Rabbeinu Yonah ibid
 The reason: As it appears like one is scoffing at the dead, as it expresses that they are poor and exempt from Mitzvos and are not able to fulfill them, while we do fulfill them. [23/1; Brachos 18a] The souls of the dead stand above their grave and are able to see the Tzitzis if they are revealed. [Arizal in Shaar Hamitzvos Vayechi; Kaf Hachaim 23/1]
Tying the Tzitzis strings to each other: Some are accustomed upon entering into a cemetery to tie the Tzitzis of two corners to each other in order to nullify the Mitzvah of Tzitzis from them [and hence allow one to enter the cemetery with the Tzitzis revealed]. However, in truth this does not help at all, as although the Tzitzis are tied to each other, nevertheless the Mitzvah of Tzitzis is not nullified through doing so, as he intends to return and untie them. [Admur 23/3; Michaber 23/2; M”A 23/1]
 The reason: As today we only wear Tzitzis [both the Tallis Gadol and Katan] for the sake of the Mitzvah and not for the sake of garbing our body, and hence it is forbidden to enter to a cemetery wearing them revealed, even if they do not drag on the grave, being that it appears to be scoffing the dead. However in previous times, it was permitted to enter with a four cornered garment that had Tzitzis so long as the Tzitzis did not drag on the actual grave, as in those times all their clothing were made with four corners and had Tzitzis attached to them. It was hence not practical to require them to remove all their clothing upon entering a cemetery. [Admur 23/1-2]
 This applies even to a Tallis Katan [Implication of Admur ibid; Bach; Perisha; Poskim in Kaf Hachaim 23/2]
Custom of Terumas Hadeshen: The Terumos Hadeshen was accustomed to remove the Tallis Katan prior to entering into a cemetery. He did not suffice with it being covered under his clothing. [Leket Yosher p. 11]
 23/4; Michaber 23/3
 Admur 45/1 regarding Tefillin and the same would apply regarding Tzitzis
Other opinions: Some Poskim rule it is permitted to enter the cemetery so long as one is a distance of four Amos from the grave. [Poskim in Kaf Hachaim ibid]
 Admur ibid; Taz 23/1; Shach Yoreh Deah 344/11; Elya Raba 23/3; M”B 45/1; See Biur Halacha 45/1; Poskim in Kaf Hachaim 23/4
The reason: As perhaps he will unknowingly enter into the four cubit radius of a grave. [ibid]
 Admur ibid; Michaber Yoreh Deah 367/6; Rashba 3/300
The reason: As the wall separates the cemetery from the outside and thus there is no apparent act of scoffing by doing so. [ibid]
Other opinions: Some Poskim rule it is forbidden to stand within four Amos of the cemetery even if he is outside the cemetery. [M”A 45/1]
 Such as was the custom in the times of the Gemara that all their clothing had four corners with Tzitzis, and they wore a second pair of Tzitzis for the sake of Mitzvah. [ibid]
 The reason: As one cannot demand of such people to remove all their clothing upon them going to a cemetery. [ibid]
 The reason: As it appears like we are scoffing the dead by showing them the Mitzvos that they cannot fulfill. [23/1]
 23/4; Michaber 23/3
 M”B 23/3 based implication of Beis Yosef
 P”M 23 [brought in M”B ibid]; implication of Bach and Perisha 23/1 in name of Rashal; Aruch Hashulchan 23/2
 Piskeiy Teshuvos 23/1
 See M”B 23/5
 The reason: As the concept of Loeg Larash and Mitzvos do not apply to a gentile.
 Elya Raba 23/3 in name of Maharitz Tzehlin [Perek Eizehu Neshech 12a]; Peri Megadim 23 A”A 2; M”B 23/5
 The reason: As they are not liable in the Mitzvah of Tzitzis anytime in their life. [M”B ibid] and we do not suspect they have a Gilgul of a male soul. [Kaf Hachaim 23/3]
 Mishneh Lemelech 13/9; Tzelach Brachos 3b; Poskim in Kaf Hachaim 23/3 that even Mahrit Tzehelin ruled its forbidden; Poskim in Pischeiy Teshuvah Yoreh Deah 367/1
 Elya Raba 23/3 in name of Maharit Tzehlin; Peri Megadim 23 A”A 2; M”B 23/5; Kaf Hachaim 23/3
 The reason: As perhaps the soul of a child is considered a Gadol. [ibid]
 Minchas Elazar 3/53; Devar Yehoshua 4/16; Tzitz Eliezer 10/10; 19/2; Piskeiy Teshuvos 23/1
 Pashut!; Piskeiy Teshuvos 23/1
 See Gesher Hachaim 2/14 for a lengthy treatise on this subject, with all the reasons and opinions mentioned.
 Michaber Y.D. 351/2 “One may not bury a corpse in a Tallis without Tzitzis” and Rama ibid “Other Poskim rule it does not require Tzitzis, although the custom is to bury him with Tzitzis”; Nemukei Yosef Tzitzis; Shesileiy Zeisim 23/6; Aruch Hashulchan 351/3 “The custom of all Jewry is to bury the corpse in a Tallis with Tzitzis”; Kaf Hachaim 23/7
The reason: Some say this is because a corpse is obligated in Tzitzis, and it is for this reason that the Parsha of Tzitzis in Shelach was taught immediately after the Parsha of the death of the Mikosheish Eitzim. [Nimueki Yosef ibid] Alternatively, the reason is to show that we believe that the corpse will be resurrected with its clothing, and hence will immediately begin to perform its Mitzvah of Tzitzis. [Soles Belula, brought in Kaf Hachaim ibid]
 Sefer Chassidim 733; Kitzur SHU”A 197/1; Mishmeres Shalom 9/22; See Sheilas Yaavetz 1/166; Pischeiy Teshuvah 351/3
 Rama ibid; Kitzur SHU”A 197/1; Aruch Hashulchan 351/3 [See there that the Gr”a and the Yesod Veshoresh Havoda asked to be buried in Kosher Tzitzis and neither Chevra Kadisha were successful in doing so due to unexplainable events.]
 Minhag Chabad brought in Nitei Gavriel 47 footnote 7; See Admur 15/5 in parentheses
 Michaber ibid; Ramban; Nemukei Yosef Tzitzis; Shesileiy Zeisim 23/6; Kaf Hachaim 23/7
 Gesher Hachaim 2/14 [See there for a very lengthy discussion on this topic]; Nitei Gavriel 47/7
 See Gesher Hachaim ibid