Davening with a Minyan and learning Torah by Kivrei Tzadikim:

It is forbidden to Daven, learn Torah, or wear Tallis and Tefillin, within four Amos of a Kever, or within a cemetery.[1] Nevertheless, the custom is to permit Davening and Torah learning near the Kever of a Tzadik, and thus we see Minyanim for prayers take place by the Kever of Rachel Imeinu, the Avos in Chevron, the Rambam, the Rebbe’s Ohel and many other Kevarim throughout the world.[2] This is permitted under several grounds, which are independent of each other: 1) The prayer that takes place by the Tzadik is done in merit of the Tzadik, and is thus considered for his benefit.[3] 2) It is common to build a Mechitza around the Kever, and it is permitted to Daven even within four Amos of a Kever if there is a Mechitza surrounding it.[4] 3) The Kevarim of the Tzadikim in Eretz Yisrael were customarily buried with an Ohel Tefach which thus prevents the Tuma from rising, and in essence separates the people from the Kever similar to a Mechitza.[5] 4) Learning and Davening by the Avos and Imahos is permitted, as they lived prior to the giving of the Torah and hence the concept of Loeg Larash does not apply to them.[6] The above allowance only applies if the Kever of the Tzadik is segregated from other Kevarim. If, however, the grave is in the midst of other graves without a Mechitza to separate between them, then it is forbidden to Daven there.[7]  

________________________________________________________________

[1] So rule regarding Shema: Admur 71:6; Bach 71; Taz 71:5; Michaber 71:7; Brachos 18a; So rule regarding Davening: Michaber Y.D. 367:3 and 6; So rule regarding Tzitzis: Admur 23/1-2; Michaber 23/1 Y.D. 367:4; So rule regarding Tefillin: Admur 45/1; Michaber 45:1; Brachos 18a

The reason: This is forbidden due to the verse [Mishleiy 17:5] “Loeg Larash Cheref Oseihu.” [Admur ibid]

[2] Chida in Shem Hagedolim Erech Elazar Ben Nasam that the custom is to Daven near the Kevarim of Tzadikim; Minchas Elazar 3:53 that the custom is to Daven with a Minyan on Rosh Chodesh with sefer Torah by Kever Rachel, and the custom dating back many generations is to Daven near the Kever of Rashbi, and that so is permitted by all Kivrei Tzadikim and so is implied from Maharit Tzulin in Chidushim to that one may Daven near the Kever of Choni Hamagil; Devar Yehoshua 4:16; Tzitz Eliezer 10:10; 19:2; Even Yaakov 36; Piskeiy Teshuvos 23:1

[3] Michaber 367:3 “Even by heart one may not read words of Torah unless it is done for the honor of the dead”; 344:17 “It is permitted to speak words of Torah in relation to the deceased and in respect of the deceased even within his four cubits.”; Kaf Hachiam 23:1 “If one learns by the Kever in honor of the deceased, there is no prohibition of “Loeg Larash,” as he is doing so for his honor.”; Minchas Elazar ibid that we Daven by Kivrei Tzaddikim in their honor and to elevate their soul and receive their assistance in elevating our prayers to Heaven; See Pesach Hadvir 45:4

Other opinions: See Tosafus Bava Kama 16b from whom it is implied that one may not learn Torah near a Kever even in honor of the deceased, unless he is a distance of four Amos from the grave. See Minchas Elazar ibid

[4] Admur 23/1-2; 45/1; 71:6; Michaber Y.D. 367:6; Rashba 3:300; Minchas Elazar ibid

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]

[5] See Emek Sheilasa 14:6 and Zekan Aaron 2:85; that since the Kever is dug more than ten Tefach, it is a different Reshus; Minchas Elazar ibid; Tzitz Eliezer ibid

[6] Minchas Elazar ibid

[7] See Tzelach Brachos 3 and 18; Minchas Elazar ibid; Piskeiy Teshuvos 23/1