A woman became pure [from menstruation] before Fajr, but did not perform ghusl until after sunrise — what is the ruling on her fast?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah ﷺ.
Her fast is valid, since ghusl (ritual bathing) is not a condition for the validity of the fast, but rather for the validity of the prayer. However, she is sinful for delaying the Fajr prayer beyond its designated time without a valid excuse.
It is known that the time for Fajr prayer ends at sunrise. Nevertheless, she must still perform ghusl, and make up the Fajr prayer. And Allah, the Exalted, knows best.
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.
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.
What is the ruling on public street water if it gets on a person's clothes or body?
The default ruling is that public street water is pure (tahir). If one is certain of its impurity (najasa), then a small amount that gets on the lower part of a person's clothes or body is overlooked (excused). And Allah the Almighty knows best.