*Regarding an interval made by a listener, and regarding an interval made by the Chazan between the blessing and reading, see next Halacha!
Lechatchilah: Initially the reader may not make any interval in middle of the reading, even if he remains silent. The Megillah is to be read straight from beginning to end without interval. One is not to delay more than a breath between each verse.
Bedieved: A Chazan who made an interval during the reading of the Megillah, such as he read a section, stopped the reading, and delayed for some time, and then continued the reading from where he left off, he has fulfilled his obligation. This applies even if the amount of time of delay was equal to [or more than] the amount of time it takes him to read the entire Megillah [from beginning to end]. [If however the Chazan made an interval due to Oness and the interval was equal or more than the amount of time it takes him to read the Megillah, then he must repeat the reading from the beginning, without a blessing. This Oness refers to one who made an interval in the reading due to a Halachic prohibition to continue the reading, such as if the reader had to use the bathroom in middle.]
Talked: Even if the Chazan stopped in middle of the reading and held a conversation, he may nevertheless continue with the reading from where he left off, and it is not considered an invalidating interval. Nevertheless this is only Bedieved, however initially the reader may not make an interval in middle of the reading and one who does so and talks is to be scolded.
Once the blessing has been recited it remains forbidden to speak or make any interval from that point and on, until the reading is complete. Nevertheless, Bedieved, if the Chazan made an interval the reading is valid, so long as the interval was not due to Oness that delayed more time than the actual reading.
May the Chazan stop during the Megillah to greet someone who deserves respect [Shoel Mipnei Hakavod]?
The Chazan may stop during Bein Haperakim, just like is the law regarding the reading of the Shema. Nevertheless it is disputed in Poskim as to the definition of Bein Haperakim. All the above is with regards to the Chazan, however the listener may never interrupt, as if he misses even one word he does not fulfill his obligation.
May the Chazan stop in different sections of the reading to explain or expound that section of the Megillah?
No. This is initially forbidden to be done.
 M”B 690/20 based on Rama ibid
 As once he has begun the blessing he may not make an interval until he completes the Mitzvah. [M”B ibid] Alternatively the reason is because the Megillah is called an Igeres [letter] and a letter is normally read from beginning to end without interval. [Levush brought in Kaf Hachaim 690/32]
 M”A 690/17; Elya Raba 690/10; M”B 690/52
 M”B 690/17; Kaf Hachaim 690/33; Even one hour. [Chayeh Adam 154/18]
 M”B 690/18; Biur Halacha 65 “Karah Seirugin”; Peri Megadim 690 A”A 7; Kaf Hachaim 690/35; based on M”A 422/9 regarding Hallel.
The reason: As the Megillah reading is given the same law as one who made an interval during Shema.
It is a dispute amongst Rishonim and Poskim in whether an interval invalidates a Mitzvah other than Shemoneh Esrei. The Rif; Rambam and Michaber 65/1 rule one never has to repeat the Mitzvah even if he made an interval due to Oness. The Tosafos; Rosh rule that if one made an interval due to Oness, that equals in time to the amount of the Mitzvah, then he must repeat the Mitzvah in all cases. The Rama rules like this opinion regarding Biblical commands [Rama and Admur 65/1] and rules like the Rif regarding Rabbinical commands. Hence according to the Rama, an interval during the reading of Megillah does not invalidate the reading. [Darkei Moshe 422] However the Levush; Olas Shabbos; Elya Raba and Bach rule like the Tosafus and Rosh even by Rabbinical commands. The M”A 422/9 concludes that by Rabbinical commands [such as Hallel] one is to repeat the Mitzvah without a blessing. [Biur Halacha ibid; Kaf Hachaim 690/35; See Kaf Hachaim 588/14]
 Admur 65/1 regarding the law by Shema
 Rama ibid; M”B 690/19 based on Rashba; Kaf Hachaim 692/22
 M”A 692/4; M”B 692/9; Kaf Hachaim 692/23
 The Shiltei Giborim [brought in Machatzis Hashekel on M”A ibid] leaves this matter in question. The Machatzis Hashekel ibid writes in the name of Lechem Chamudos that between each Parsha Setuma or Pesuacha is considered Bein Haperakim. Rav Shlomo Kluger rules that Bein Haperakim is defined as from the beginning until Ish Yehudi and from Ish Yehudi until Ublayla Hahu. [Shaar Hatziyon 692/11] The P”M 692 A”A 4 rules that possibly between verses is considered Bein Haperakim. [Kaf Hachaim ibid]
 Kaf Hachaim ibid; M”B ibid
 Based on Rama 690/5; M”B 690/46; 692/9. However from Michaber 690/13 it is implied that it is even initially allowed. Vetzaruch Iyun