What should a person who was favored from Allah with a newborn, but couldn`t afford an Aqeeqah, do?

Aqeeqah (the sheep slaughtered on the seventh day from the child`s birth) is a desirable Sunnah for the financially able since Allah, The Exalted, charges not a soul beyond its capacity. Therefore, if the father couldn`t afford the Aqeeqah before the end of his wife`s confinement, then it isn`t due on him, and if he was able to afford it later on, then it is permissible, but if he didn`t until the child reached puberty, the latter can offer the Aqeeqah himself.

What should a mensurating woman, or in state of confinement do if she became ritually pure during the daytime of Ramadhan ?

If she became pure during the daytime of Ramadhaan, is desirable to complete her fasting during that day, and to make up for it along with other missed days due to menstruation. And Allah Knows Best.

What is the ruling on performing voluntary prayers during official working hours?

All perfect praise be to Allah, The Lord of The Worlds, and may His Peace and Blessings be upon our Prophet Muhammad and upon all of his family and companions

There is no harm if  there was break time during official working hours, but if not then it is impermissible. And Allah Knows Best.

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.