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May one recite the 13 attributes of mercy to himself in the Torah reading tune?
If one is saying Selichos without a Minyan, he is to omit the 13 attributes of mercy. It is permitted to recite the thirteen attributes in the Torah reading tune even if one is reciting it alone. Nevertheless, many are accustomed to avoid doing so, and they thus completely omit it when a Minyan is not present. Practically, the recorded Chabad custom is not to say it.
If one is behind the Minyan and the congregation has reached the 13 attributes of mercy what is he to do?
The custom is to stop and read the 13 attributes together with the congregation, as is the law by Kaddish and Kedusha. This applies for everyone in the Shul, even if one is not part of the Minyan for Selichos. Nevertheless if one is in the midst of prayer, and is in an area that he cannot make an interval, then he is not to say it.
If one is Davening with a Minyan and the congregation has already recited the 13 attributes of mercy may he recite it when he reaches that point?
No. The 13 attributes of mercy may only be recited together with the actual Minyan.
Must one read each word of the 13 attributes together with the congregation or can he read it on his own pace?
If one begins reading the 13 attributes together with the congregation, and the congregation is saying the words quickly, it is permitted for him to recite the words at his own pace.
If the congregation is already in middle of reciting the 13 attributes may one begin to say it?
Some write that as long as majority of the congregation has not yet completed the recitation, then he may recite it with them.
 Michaber 565:5; Mateh Efraim 581:21; Kaf Hachaim 565:26 [this applies even during the Aseres Yimei Teshuvah].
 Michaber 565:5; Tur 565; M”A 565:5; Rashba in Teshuvah; Terumas Hadeshen 8; Seder Hayom [must finish the entire verse]; Machazik Bracha 131:6; Kesher Gudal 19:9; Ruach Chaim 131:1; Mateh Efraim 581:21 [however states that in such a case must omit the words Zechor Lanu Hayom Bris Shlosh Esrei]; Hisorerus Teshuvah 2:140; Minchas Elazar 4:22 [defends ruling of Mateh Efraim however in Darkei Chaim Veshalom 190 says not to say at all even in a way of Niggun. Vetzaruch Iyun.]; Grach Naah in Yagdil Torah Jerusalem 17 p. 26 [states that technically one is not even required to recite it with the tune]; Igros Moshe Yoreh Deah 3:10; Kaf Hachaim 131:23 brings the dispute on this matter and rules it is only to be said with the Niggun by Tachanun and not by Selichos.
The reason: As there is no prohibition in reading it as a verse in scripture. The prohibition is only when reading it without a Minyan as a prayer and supplication
The tune: Rav Avraham Chaim Naah in Yagdil Torah ibid states that technically one is not even required to recite it with the tune, and it is only done to show that one does not mean to say it as a prayer. The Igros Moshe ibid similarly states that one may read the words in the usual tune he uses for reading words of Torah, even if it is not the actual Torah reading tunes [Taamim], so long as it does not sound like a supplication.
Finishing the verse: The Seder Hayom writes that one must finish the entire verse [until Vieal Riveim] and may not stop by the words Venakeh, as it is forbidden to end a verse in an area that Moshe did not end. [see Admur 494:11] However, some Poskim state it is not necessary to finish the verse. [Ben Ish Chaiy in Rav Poalim 1:11; Yechaveh Daas 1:47 based on Pesach Dvir 51] Practically, the Kaf Hachaim ibid negates the opinion of the Seder Hayom, and so rules Rav Avraham Chaim Naah in Yagdil Torah ibid; Igros Moshe ibid; Hisorerus Teshuvah 2:140; Piskeiy Teshuvos 565:5]
Reading in a Siddur: Some write that one must read the verse within a Sefer rather than from memory. [Piskeiy Teshuvos ibid in name of Peri Hasada 4:49]
 Beis Yosef 565; Taz 565:5; Birkeiy Yosef 488:5 in name of Maharam Zakusa in name of Arizal; Shalmei Tzibur p. 148; Zechor Leavraham 131:7; Darkei Chaim Veshalom 190 [However see Minchas Elazar 4:22 who defends ruling of Mateh Efraim ibid that it may be said so long as one skips the parts that mention the 13 Middos before and after reading it. Vetzaruch Iyun.]; Kaf Hachaim 131:23 rules that by Selichos one may not say it.
The reason: The reason is because since he is mentioning it at this time, seemingly his intent is as a request and not to read a verse in the Torah. [Taz ibid]
 Otzer Minhagei Chabad Elul 63; Hiskashrus 423 p. 18 footnote 17; Glosses of Rav Raskin on Siddur footnote 337; Heichal Menachem 3:265
Otzer Minhagei Chabad ibid records that an individual does not recite the 13 attributes even with the Torah reading tune. This is based on an answer of the Rebbe to this exact question of which the Rebbe answered that he has not heard of such a practice of reading it with the tune. In the first printings of the Siddur Tehillas Hashem it stated by Mincha that a Yachid does not recite the 13 attributes. It did not mention this by Shacharis or Selichos. The Rebbe was hence asked if there is a difference, to which the Rebbe replied in Igros Kodesh 3:138 that he never heard of such a differentiation as the ruling is clearly given in 565:5 without any difference regarding the type of prayer.
 Sheivet Halevi 7:12; Igros Moshe 3:89; Yabia Omer 4:8; Piskeiy Teshuvos 131:9; See Sheivet Halevy 9:1; Kinyan Torah 4:9
 This matter is disputed in Poskim regarding whether the 13 Middos have the same status as any Davar Bekedusha or not. See Halef Lecha Shlomo 44; Tehila Ledavid 66:7; Igros Moshe ibid; Yabia Omer ibid. Practically the age old custom is to treat it as a Davar Shebekidusha.
 Poskim ibid
 Sheivet Halevy 9:1; Kinyan Torah 4:9
 Sheivet Halevi 7:12; 9:24; Piskeiy Teshuvos 131:9; 581 footnote 78; However see Torah Leshma 96 that he writes if the Yachid began viduiy together with the congregation then he may continue and start the 13 attributes even after they finish.
 As it is considered a Davar Shebekedusha and is similar to Kaddish and Kedusha which may only be recited with ten people at the same time. [See M”B 565:11]
 Ben Ish Chaiy Ki Sisa 4 as explained in his Sefer Mikavtzel; Torah Leshma 96; Kaf Hachaim 131:24
 As since one began saying the words with a Minyan he may finish it off. [ibid]
 Piskeiy Teshuvos 131:9 [however the sources he provide are inaccurate] The Ben Ish Chaiy ibid only relates to a case that one began with the congregation. However in Torah Leshma 96 he writes that if the Yachid began viduiy together with the congregation then he may continue and start the 13 attributes even after they finish.