Is it necessary to offer another 'aqiqah for the girl and the boy after a monetary amount equivalent to the price of the 'aqiqah was given, and is it permissible to combine their 'aqiqah, and what is the manner of the 'aqiqah, and should it be cooked at home or distributed as meat?

The 'Aqiqah is recommended, not obligatory. Its value cannot be given in cash; rather, a sheep must be slaughtered for each child. It is preferable to slaughter two sheep for a male and one for a female, though one sheep is sufficient for a child. It is recommended to cook the 'Aqiqah and give some or all of it as charity. It is permissible to slaughter it in any country by appointing someone to act on your behalf.