What is the ruling on eating and drinking at night after making the intention? Is it necessary to renew the intention?
Eating and drinking at night, even after making the intention (for the next day), does not affect the fast, and it is not necessary to renew the intention after eating and drinking.
Does burping (belching) break the fast?
Burping does not break the fast. However, if anything comes up from the stomach, the fasting person must spit it out and rinse their mouth to cleanse it.
If they swallow it intentionally while being able to expel it, or if they swallow their saliva before rinsing their mouth, their fast is invalidated.
Should the Zakah (obligatory charity) giver tell the poor recipient that this is the Zakah of his money?
No, he shouldn`t. But, the Zakah giver should make an intention in his heart that it is the Zakah of his money when paying it to the poor. And Allah Knows Best.
What is the expiation for perjury?
One who commits perjury should repent, seek Allah`s forgiveness and offer an expiation which is: feeding ten indigent persons, or clothing them, or giving a slave his freedom, but if that is beyond his means then, he should fast for three days. Allah, The Almighty, Says in this regard (What means): "Allah will not call you to account for what is futile in your oaths, but He will call you to account for your deliberate oaths: for expiation, feed ten indigent persons, on a scale of the average for the food of your families; or clothe them; or give a slave his freedom. If that is beyond your means, fast for three days. That is the expiation for the oaths ye have sworn. But keep to your oaths. Thus doth Allah make clear to you His signs, that ye may be grateful." [Al-Ma`idah/89].