Early prayer times?

[Nizam1]

I've been looking at prayer times for the coming months and I've seen that Fajr prayer is sometimes offered very early in the morning (2.35am for example).

So my questions are this:

a) Have I got this completely wrong? (I hope not, if I have then I may well have made a mess of things)

b) Assuming I have got things correct, how do those of you with children, and especially young children, go about this?

Thanks

[sur]

Fajr: Dawn -till- before sun starts to rise out of horizon.
Zuhr:Sun crosses vertex of sky(Bukhari:12:738) -till- shadow of stick equals twice it's length.
Asr: Shadow of stick equals twice it's length -till- sun starts to set.
Maghrib: Sun completely set(Bukhari:10:536)-till- Yellow/Red/Orange light at horizon gone.
Isha: After Maghrib -till- preferrably midnight.



Sahih Bukhari:10:536:Narrated Salama: We used to pray the Maghrib prayer with the Prophet when the sun disappeared from the horizon.

Bukhari:10:557
Allah's Apostle said, 'Do not pray at the time of sunrise and at the time of sunset.' " Ibn 'Umar said, "Allah's Apostle said, 'If the edge of the sun appears (above the horizon) delay the prayer till it becomes high, and if the edge of the sun disappears, delay the prayer till it sets (disappears completely).' "


Sahih Bukhari:12:738:Narrated Saiyar bin Salama: My father and I went to Abu Barza-al-Aslami to ask him about the stated times for the prayers. He replied, "The Prophet used to offer the Zuhr prayer when the sun just declined from its highest position at noon; the 'Asr at a time when if a man went to the farthest place in Medina (after praying) he would find the sun still hot (bright). (The sub narrator said: I have forgotten what Abu Barza said about the Maghrib prayer). The Prophet never found any harm in delaying the 'Isha' prayer to the first third of the night and he never liked to sleep before it and to talk after it. He used to offer the morning prayer at a time when after finishing it one could recognize the person sitting beside him and used to recite between 60 to 100 verses in one or both the Rakat."

Malik Mauta:1:9:-Yahya related to me from Malik from Yazid ibn Ziyad that Abdullah ibn Rafi, the mawla of Umm Salama, the wife of the Prophet, may Allah bless him and grant him peace, asked Abu Hurayra about the time of the prayer. Abu Hurayra said, "Let me tell you. Pray dhuhr when the length of your shadow matches your height, asr when your shadow is twice your height, maghrib when the sun has set, isha in the first third of the night, and subh in the very first light of dawn," i.e. when the dawn has definitely come.