Which hour coincides with the last third of the night?
This hour could be figured out by calculating the number of night hours which start at sunset, and end at dawn break, then the total is divided on three to get the result.
Who should pay the Zakah (obligatory charity) from the orphan`s money?
His/her guardian, and if the latter fails to do so, then the orphan himself/herself is obliged to pay the Zakah once he/she reaches puberty, and is capable of handling his/her own affairs. And Allah Knows Best.
When is supplication (du‘a) more likely to be accepted: before or after breaking the fast in Ramadan?
Du‘a is accepted at all times, and this is part of Allah’s mercy and generosity toward His servants.
The Prophet ﷺ said: "No Muslim makes a supplication that does not involve sin or severing family ties except that Allah grants them one of three things: either He grants their supplication immediately, or He stores it for them in the Hereafter, or He averts from them an equivalent harm." [Narrated by Ahmad]
However, in Ramadan, du‘a is especially likely to be accepted shortly before breaking the fast.
The Prophet ﷺ said: "Three supplications are never rejected: the supplication of a fasting person until they break their fast, the supplication of a just leader, and the supplication of an oppressed person. Allah raises it above the clouds, opens the gates of heaven for it, and says: ‘By My might, I will surely grant you victory, even if after a while.’" [Narrated by Al-Tirmidhi]
Is Fajr (dawn) Sunnah a confirmed one?
All praise be to Allah The Lord of The Worlds Of course, it is a confirmed Sunna which the Prophet (PBUH) used to offer in a regular basis. And Allah Knows Best.