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.

 Reciting the Prophetic narration is permissible as many scholars used to, since in principle, the rulings of recitation have to be observed while speaking Arabic language.

What should a woman who delayed making up for missed fast, due to menstruation, till the start of the next Ramadhaan ?

Whosoever broke fasting in Ramadhaan, and was able to make up for it, but didn`t until the next Ramadhaan started, is obliged to make up for the missed days, and to pay the ransom as well. However, if he/she wasn`t able to before next Ramadhaan due to an excuse, then he/she should only make up for the missed days .

Is it permissible for one to shake hands with his uncle`s daughter?

No, it isn`t because he is a non-Mahram(Marriageable) to her.