When is Hallel to be recited?
From when during the day, and until when in the day: Hallel may be recited throughout the entire day, from dawn [Alos Hashachar] until nightfall [Tzeis Hakochavim]. Thus, if one did not recite Hallel immediately after Davening [Shemoneh Esrei of] Shacharis, he may recite it throughout the day, until Tzeis Hakochavim.
May one initially read Hallel before sunrise? Lechatchilah one should not recite Hallel prior to sunrise. Nevertheless, if one transgressed and recited Hallel prior to sunrise, after daybreak he has fulfilled his obligation.
After Shemoneh Esrei: Although Hallel may be recited throughout the day, it is best to recite it immediately after the Shacharis Shemoneh Esrei. [It is permitted to recite Hallel prior to Davening Shacharis. Nevertheless, according to the Arizal, Hallel is not to be said prior to Davening.]
May Hallel be recited with a blessing after sunset, prior to nightfall?
No. One is to recite Hallel without a blessing.
May one eat before Hallel?
One is to avoid eating prior to reciting Hallel, unless he is sick or weak in which case he is not to be stringent even as an act of piety. [Thus, even if one already Davened Shacharis but has not yet recited Hallel, he should avoid eating until he recites Hallel.]
 Admur 488:3; Mishneh Megillah 20b
 Admur ibid; See also regarding Shofar: 588:1; Michaber 588:1
 The reason: As it appears like night in the eyes of the masses. [ibid] In 588:1 Admur writes as follows regarding Shofar: Biblically, day begins from Alos Hashachar regarding all Halachic matters. Nevertheless, the Sages decreed that one must delay blowing the Shofar until after sunrise being that not all people are expert in the definition of Alos and hence in order to be certain that it is day, one must wait until sunrise. [Admur ibid; Rashi Megillah ibid]
 Admur 131:5 in parentheses; See Rosh Hashanah 32b; Megillah 20b; 156:17
 The reason: As Zerizin Makdimim Lemitzvos. [ibid]
 See Admur 488:3, brought in next Halacha; Vetzrauch Iyun as to why even initially Hallel was not established to be recited prior to Shacharis. Perhaps the reason is because Hallel may only be recited after sunrise while one may Daven up until Shemoneh Esrei prior to sunrise.
 Shalmei Tzibur 223; Beis Oved 6; Kaf Hachaim 422:38
 Nitei Gavriel Chanukah 49:5; Regarding Shofar: Chayeh Adam 141:1; 144:20; Mishneh Berurah 588:1; Kaf Hachaim 588:2; 600:12; Regarding Lulav: M”A 658; Regarding Megillah: M”B 687:5; Kaf Hachaim 687:9; P”M 692 M”Z 3
Opinion of Admur: Admur ibid rules that from Alos until Tzeis is the permitted time for reciting Hallel. So writes Admur also regarding Shofar in 588:1 and 18:8 regarding Tzitzis. The source of Admur is from the Gemara Megillah 20b which states that until Tzeis Hakochavim it is considered day. This seems to imply that during Bein Hashmashos one may recite Hallel and blow Shofar even with a blessing! This is further inferred from the change of wording from the Tur 588 which writes simply “until night” while Admur specifies Tzeis. Vetzaruch Iyun Gadol, as Bein Hashmashos is questionable whether it is night or day as rules Admur is 261:1, hence how can one say a blessing at that time. Practically, the Poskim rule one is to not recite a blessing past sunset. Likewise, in the Siddur Admur retracted his ruling regarding Tzitzis, and rules the blessing may not be recited after sunset.
 Sheilas Yaavetz 40; Birkeiy Yosef 422:5; Shaareiy Teshuvah 422:5; Kaf Hachaim 422:30