Is it permissible for a suitor to go out with his fiancé upon the conclusion of the marriage contract?
Upon the conclusion of the marriage contract, the woman becomes lawful for her husband. However, the customary practice should be observed in this regard since rights could be lost in case of divorce, or death.
When does the time for the 'aqīqah lapse and pass?
All praise is due to Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
If the guardian was financially capable (mūsir) during the majority of the postnatal period (nifās) — which is sixty days — then the obligation of the 'aqīqah remains upon him until the child reaches the age of maturity (bulūgh). Once the child reaches maturity, the demand falls away from the father and those like him. At that point, it becomes Sunnah for the child himself to perform the 'aqīqah on his own behalf.
However, if the guardian was financially incapable (mu'sir) during the postnatal period, and then became financially capable after its expiry — that is, after sixty days — the 'aqīqah is no longer required of him. And Allah Almighty knows best.
When is Istikharah (guidance prayer) Du`a offered, before Tasleem (saying asalamu alikum warahmatu allah wa barakatuh to end the prayer), or after it?
It is offered after Tasleem.
What is the amount of the Fitr Zakah (obligatory charity) of Ramadan?
The Fitr Zakah of Ramadhaan is a Sa` (2500 grams) from what the people of that country or state eat the most. And Allah Knows Best.