Is the Megillah read with its blessings in Jerusalem on Friday the 14th of Purim Meshulash, if a Minyan is not present?
A. The general rule:
One must always strive to hear the Megillah reading in the presence of a Minyan, which consists of at least ten adult men. If one cannot find a Minyan for the Megillah reading, then it is to be read without a Minyan. Even when reading the Megillah without a Minyan one is to recite the blessings that are said prior to the Megillah reading. [However, the after blessing [i.e. Harav Es Riveinu] may not be recited when reading without a Minyan.] This ruling however that a blessing is to be said even without a minyan is only applicable in the case that the Megillah is being read by its set and established date, otherwise it is under debate as to whether a blessing may be recited if a minyan is not present. Now, it is under question as to how to view the date of the Megillah reading in Jerusalem when it is preceded to Friday the 14th and as to whether it is viewed as its set date or not. The following are the full details of the subject as discussed in the Poskim, as to whether Jerusalem residents may read the Megillah with a blessing on Friday the 14th even if it minyan is not present:
B. The law in Jerusalem on Purim Meshulash:
According to many Poskim, Jerusalem residents who normally celebrate on the 15th and are now celebrating Purim Meshulash and reading the Megillah on Friday the 14th, may only read the Megillah with its blessings if there is a Minyan present. If a Minyan is not present, then the Megillah is read on Friday without a blessing [i.e. neither the blessings of Al Mikra Megillah, nor Sheasa Nissim, nor Shehechiyanu]. Other Poskim, however, argue on this and rule that even in Jerusalem in such a year that the Megillah is read on the 14th, it may be read with its blessings even without a minyan, if necessary. Practically, while the leaning arbitration in such a debate would be to follow the rule of Safek Brachos Lihakel and hence not recite blessings in such a situation that a minyan is not present, nonetheless being that the testified custom of Jerusalem is to recite a blessing even in such a case, therefore one who does so has upon whom to rely. Whatever the case, it goes without saying that in order to circumvent the above debate, Jerusalem residents must take extra care and effort by a year of a Purim Meshulash to try to be by a minyan for the Megillah reading. Also, to note that the above discussion is only regarding the before blessings over the Megillah reading, however the after blessing of Harav Es Riveinu is never recited without a minyan present as already explained in chapter 7 Halacha 10. See there for the full details of this subject!]
C. The law by doubtful cities who normally read on two days:
The above debate and discussion is only relevant Jerusalem residents, while residents of all other cities, including cities that during normal years keep two days due to doubt, read the Megillah with its before blessings even if a minyan is not present on Friday the 14th.
 See Purim Meshulash [Deblitzky] 2:11 footnote 28 in great length
 Michaber 690:18
The reason: The Rama learns that the reason for this is in order to publicize the miracle within the city, and a public matter needs to be done in front of ten people. [so is implied from Rama ibid]
 Michaber ibid
Other Opinions: Some Rishonim [Mordechai; Bahag; Geonim brought in Orchos Chaim] rule that one is not obligated to read the Megillah if he does not have a Minyan. See Kaf Hachaim 690:124
 Rama ibid: “When an individual reads the Megillah in its proper time he needs to say a blessing over it”. So rules: Rambam; Beis Yosef in name of all Poskim; Teshuvos Maharil 56; M”B 692:8: “According to all one must say the before blessings”.
Other Opinions: Some Rishonim [Mordechai; Bahag; Geonim brought in Orchos Chaim] rule that one is not obligated to read the Megillah if he does not have a Minyan, hence in their opinion it is forbidden to say a blessing. Some Poskim conclude that one is to suspect for this opinion, especially regarding blessings, and not recite a blessing when reading the Megillah without a Minyan. [Rabbeinu Yerucham 57; See Kaf Hachaim 690:124]
 Rif, Rashba, Ramban=No; Rashi and Razah=Yes
 Peri Chadash 690; Pnei Meivin 228; Shulchan Gavoa 690:40; Chug Ha’aretz 3; M”B 690:61 and Shaar Hatziyon 690:59:61 based on Gemara Megillah and opinion of Rishonim [Rif, Rashba, Ramban] in Rav and Ras Assi; Kaf Hachaim 690:118 brings all opinions and concludes Safek Brachos Brachos Lihakel; Rav Tukichinsky in Sefer Eretz Yisrael and his Luach writes not to receite a blessing [Unlike his ruling in Ir Hakodesh Vehamikdash 26b where he concludes it may be said]
 Kaf Hachaim ibid
 The reason: As there is a debate amongst Rishonim as to whether a minyan is required in order to be allowed to read the Megillah with its blessings when the readings is taking place outside of its set date [Rif, Rashba, Ramban=No; Rashi and Razah=Yes], and practically we conclude that it may not be read with its blessings. Now, the implication the Talmud is that when the Megillah reading date in Jerusalem is preceded to a Friday on the 14th it is actually considered to be not on time, even though this is the precise time the sages established for such an occurrence, and therefore nonetheless it would be subject to the above debate as to whether a minyan is required in order for a blessing to be allowed to be said over the reading. [Peri Chadash ibid and Shaar Hatziyon ibid]
 Kol Eliyahu 2:28; Bnei Binyamon p. 104, brought in Kaf Hachaim ibid; Purim Meshulash Zonenfeld 3; Salmas Chaim 1:102-103; Rav Tukichinsky in Ir Hakodesh Vehamikdash 26b [unlike his ruling in Sefer Eretz Yisrael and his Luach]; Chazon Ish 155:2; Moadim Uzmanim 1:97; Purim Meshulash [Deblitzky] 2:11 footnote 28
 The reason: As in truth when the Megillah reading date in Jerusalem is preceded to a Friday on the 14th it is actually considered to be on time as this is the time of the reading the whole world, and is hence not relevant at all to the debate mentioned above regarding a blessing may be said without a minyan when the reading does not take place on time. [Kol Eliyahu ibid]
 So concludes Kaf Hachaim ibid, as aside for the general rule of Safek Brachos Lihakel in the above debate of whether we consider the 14th for Jerusalem outside of the set date, we must also take into account the general debate of whether even a set date city may recite blessings if a minyan is not present, and hence although regarding this we are lenient certainly we should be stringent regarding the above case in which it is perhaps defined as not the set date.
 Kaf Hachaim ibid concludes that a place with an established custom to say a blessing even without a minyan may continue to do so without protest; All the following Sefarim and Poskim conclude the blessing may be said: Purim Meshulash Zonenfeld 3; Salmas Chaim 1:102-103; Moadim Uzmanim 1:97; So concludes Purim Meshulash [Deblitzky] 2:11 footnote 28 in great length that the blessings may be recited due to many reasons of argument, and due to the testified custom of the rabbis of Jerusalem, including Rabbi’s Yosef Chaim Zonnenfeld, Sefer Bnei Binyamon in name of Badatz of Jerusalem from year 5514, 5521, Chug Ha’aretz 3 that so he witnessed by Rabbanei Yerushalayim that they did not protest a blessing being said
 See Michaber 688:4