What is the expiation for perjury?

Perjury is forbidden and one of the major sins that require turning to Allah in repentance, seeking His forgiveness, giving back rights to whom they belong, or seeking their forgiveness, and expiating for that oath.

I see horrible dreams although I perform the prescribed prayers, what do you make of that?

All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.

Be mindful of Allah while awake and he will safeguard you from whatever evil you see while asleep. We advise you to make the pre-sleep supplications. And Allah The Almighty Knows Best.

Is it permissible for a Muslim to slaughter an Aqeeqah on behalf of someone else, and offer it to him as a gift?

In principle, the guardian is the one who should offer the Aqeeqah (the sheep slaughtered on the seventh day from the child`s birth) because he is obliged to provide for the newborn, and it is impermissible for anyone else to slaughter it on his behalf unless with his consent. However, it is permissible for a person to offer the sheep, or its price as a gift to the guardian of the newborn, and then the latter can slaughter it, or deputies someone else to do that on his behalf.

Is the `Iddah (waiting period) of the divorced effective from the time the divorce took place, or from the time of registering it at the court?

It is considered effective from the very moment her divorce took place, but not from the time of registering it at the court. And Allah Knows Best.